This is an open-label, multicenter, dose-escalation study designed to assess the safety, tolerability, and pharmacokinetics of oral GDC-0032 administered in combination with either docetaxel or with paclitaxel. Patients treated with the GDC-0032 and docetaxel have HER2-negative locally recurrent or metastatic breast cancer or non-small cell lung cancer (NSCLC). Patients treated with the GDC-0032 and paclitaxel combination have human epidermal growth factor receptor 2 (HER2)-negative locally recurrent or metastatic breast cancer. There are two potential stages within each arm of this study: a dose-escalation stage (Stage 1) and a dose-expansion stage (Stage 2). Once the maximum tolerated dose of GDC-0032 in a given arm has been established from dose escalation, additional patients with each combination will be enrolled in Stage 2.

Inclusion Criteria:

• Age >=18 years
• For paclitaxel combination arms: histologically or cytologically documented adenocarcinoma of the breast with locally recurrent or metastatic disease
• For docetaxel combination arms: histologically or cytologically documented adenocarcinoma of the breast with locally recurrent or metastatic disease or histologically documented advanced (Stage IV) or recurrent NSCLC
• For participants with breast cancer: HER2-negative disease as defined by local clinical guidelines
• Participants with NSCLC to be treated with docetaxel need to have received at least one prior anti-cancer treatment regimen in an advanced setting and to have docetaxel be considered appropriate treatment
• Evaluable or measurable disease per response evaluation criteria in solid tumors (RECIST) v.1.1
• Life expectancy >=12 weeks
• Eastern cooperative oncology group (ECOG) performance status of 0 or 1 at screening
• Adequate hematologic and end organ function
• Use of highly effective form of contraception

Exclusion Criteria:

• Prior anti-cancer therapy
• Prior treatment with phosphoinositide 3-kinase (PI3K) inhibitor
• Known significant hypersensitivity to any components of study treatment
• Grade >=2 peripheral neuropathy
• Type 1 or Type 2 diabetes
• Grade >=2 hypercholesterolemia or hypertriglyceridemia
• Congenital long QT syndrome
• Active congestive heart failure or ventricular arrhythmia