The goal of this clinical research study is to find the highest tolerable dose of the combination of pazopanib and vorinostat that can be given to patients with advanced cancer. The safety of the drug combination will also be studied.

Study Drugs:

Pazopanib is designed to block the growth of blood vessels that supply nutrients needed for tumor growth. This may prevent or slow the growth of cancer cells.

Vorinostat is designed to cause chemical changes in different groups of proteins that are attached to DNA (the genetic material of cells), which may slow the growth of cancer cells or cause the cancer cells to die.

Study Groups:

If you are found to be eligible to take part in this study, up to 12 dose levels of pazopanib and vorinostat will be tested. Three (3) to 6 participants will be enrolled at each dose level of the combination of pazopanib and vorinostat. The first group of participants will receive the lowest dose level of pazopanib and vorinostat. Each new group(s) will receive a higher combination dose of pazopanib and vorinostat than the group before it, if no intolerable side effects were seen. Participants may be enrolled on 1-3 similar dose levels of pazopanib and vorinostat at the same time. You will be assigned to a dose level based on when you joined this study. This will continue until the highest tolerable dose(s) of the study drug combination is found.

The dose of the study drug combination that you receive may be lowered if you have intolerable side effects.

Once the highest tolerable dose of pazopanib and vorinostat is found, this combination dose will be given to an expansion group of 14 additional participants.

Study Drug Administration:

You will take pazopanib and vorinostat by mouth 1 time each day. Note that you will not take the study drugs at the same time as each other. You should take pazopanib either 1 hour before or 2 hours after eating a meal. You should take vorinostat with food.

Study Visits:

Each study cycle is 28 days.

At all study visits, you will be asked about any drugs you may be taking and side effects you may be having.

If you are able to take your blood pressure at home, you will be asked to take your blood pressure each day while you are participating on this study.

Within 7 days before the first dose of study drugs:

• You will have a physical exam, including measurement of your weight and vital signs (blood pressure, heart rate, temperature, and breathing rate).
• You will be asked how well you are able to perform the normal activities of daily living (performance status).
• Blood (about 2 teaspoons) and urine will be collected for routine tests.
• If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.

Every week during Cycle 1, blood (about 1 teaspoon) will be drawn for routine tests.

During Week 1 of each cycle:

• Your medical history will be recorded.
• You will have a physical exam, including measurement of your weight and vital signs.
• Your performance status will be recorded.
• Blood (about 2 teaspoons) and urine will be collected for routine tests.

At the end of Cycle 2 and then every 2-3 cycles after that:

• You will have a CT, MRI, positron emission tomography (PET) scan, and/or x-ray to check the status of the disease.
• If the study doctor thinks it is needed, blood (about 1 teaspoon) will be drawn to measure tumor markers.

After Cycle 6, you are only required to visit MD Anderson every 2 cycles if you get your blood draws at your local doctor at the beginning of each cycle. Talk to the study staff about this option.

Length of Study:

You may continue taking the study drugs for as long as the doctor thinks it is in your best interest. You will be taken off study early if the disease gets worse, or you have intolerable side effects.

Your participation on the study will be over once you have completed the end-of-study visit.

End-of-Study Visit:

Within 30 days after your last dose of study drugs, you will have an end-of-study visit. At this visit, the following tests and procedures performed:

• Your medical history will be recorded.
• You will have a physical exam, including measurement of your weight and vital signs.
• Your performance status will be recorded.
• Blood (about 2 teaspoons) and urine will be collected for routine tests.
• If the study doctor thinks it is needed, blood (about 1 teaspoon) will be drawn to measure tumor markers.
• If the study doctor thinks it is needed, you will have a chest x-ray, CT, MRI, and/or PET scan to check the status of the disease.

Up to 174 evaluable patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with advanced cancer, either refractory to standard therapy or for which no effective standard therapy that increases survival for at least 3 months is available.
2. Patients must have measurable or evaluable disease, as defined by RECIST 1.1.
3. Men or women aged >/= 18 years. However, patients who are 13 years old or older and have more than 45 kg of body weight will be eligible after consultation with their pediatric attending since the doses of these agents are the fixed doses.
4. Women of child-bearing potential and men must agree to use adequate contraception.
5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
6. Adequate organ functions: Neutrophils > 1000/uL, Platelets >/= 75,000/uL, Total bilirubin </= 2 x upper limit of normal (ULN) (upper limit of normal), ALT </= 2.5 x ULN or </= 5 x ULN if liver metastases persist, Serum creatinine < 2 x ULN
7. Patients with either previous vascular endothelial growth factor (VEGF) inhibition based treatment or previous vorinostat based treatment are eligible. However, patients who received both VEGF and histone deacetylase (HDAC) inhibition simultaneously are ineligible.
8. Specific to the cohorts as designed to enroll patients with TP53 mutations: TP53 mutations are identified by next-generation sequencing in a chemiluminescence immunoassay analyzer (CLIA)-certified laboratory prior to screening.

Exclusion Criteria:

1. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring intravenous antibiotics, symptomatic congestive heart failure (NYHA Class III or IV), or unstable angina pectoris.
2. Inadequately controlled hypertension (defined as systolic blood pressure >or = 140 and/or diastolic blood pressure > or = 90 mmHg on antihypertensive medications), any prior history of hypertensive crisis or hypertensive encephalopathy, and history of myocardial infarction or unstable angina within 6 months prior to study enrollment.
3. History of stroke or transient ischemic attack within 6 months prior to study enrollment.
4. Major surgical procedure within 28 days prior to study enrollment.
5. History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to study enrollment.
6. History of allergic reactions to the study drugs, their analogs or any component of the products.
7. Any treatment specific for tumor control within 3 weeks of study drugs; or within 2 weeks if cytotoxic agents were given weekly (within 6 weeks for nitrosoureas or mitomycin C), or within 5 half-lives for targeted agents with half lives and pharmacodynamic effects lasting less than 5 days (that includes but is not limited to erlotinib, sorafenib, sunitinib, bortezomib, and other similar agents). Palliative radiation immediately before or during the study is acceptable provided there is evaluable disease that has not been radiated.
8. Urine for proteinuria >/= 2+ (patients discovered to have >/= 2+ proteinuria on urinalysis at baseline should undergo a 24 hour urine collection and must demonstrate \