This is a Phase 1 study during which patients with advanced/metastatic solid tumors will receive investigational study drug ARRY-334543 and docetaxel (with prophylactic growth factor support). Patients will receive increasing doses of study drug in combination with docetaxel in order to achieve the highest dose of study drug possible that will not cause unacceptable side effects. Patients will be followed to see what side effects the combination causes and what effectiveness the combination has, if any, in treating the cancer. Approximately 30 patients from the US will be enrolled in this study.

Key Inclusion Criteria:

• Histologically or cytologically confirmed diagnosis of any advanced/metastatic solid tumor suitable for treatment with docetaxel.
• Tumor recurred or progressed following at least one line of chemotherapy, except if no standard of care exists or if the patient refuses standard of care treatment.
• Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0, 1 or 2.
• Must be able to take and retain oral medications.
• Other criteria exist.

Key Exclusion Criteria:

• Active concomitant malignancies.
• Uncontrolled or symptomatic brain metastases (if a patient has brain metastases and is on steroids, the steroid dose must be stable for at least 30 days prior to study start).
• Known positive serology for the human immunodeficiency virus (HIV), hepatitis B and/or hepatitis C.
• Requiring intravenous (IV) alimentation.
• Pregnancy or lactation.
• Chemotherapy, anticancer immunotherapy, monoclonal antibodies or biologics within 21 days prior to first dose of study drug.
• Anti-ErbB1 and/or ErbB2 targeted therapy or anticancer hormonal therapy within 14 days prior to first dose of study drug.
• History of hypersensitivity to or intolerance of docetaxel.
• Other criteria exist.