Randomized Study Comparing Docetaxel Plus Dasatinib to Docetaxel Plus Placebo in Castration-resistant Prostate Cancer

Inclusion Criteria: * History of histologically diagnosed prostate cancer * Evidence of metastatic disease by any 1 of the following: computed tomography scan, magnetic resonance imaging, bone scan, or skeletal survey * Evidence of progression, as defined by 1 of the following: rising prostate specific antigen levels at least 1 week apart with the final value being \>=2 ng/mL; progression of measurable nodal or visceral disease, with nodal lesions \>=20 mm and visceral lesions measurable per response evaluation criteria for solid tumors (Response Evaluation in Solid Tumors, version 1); 2 or more lesions appearing on bone scan compared with previous scan; or local recurrence in the prostate or prostate bed * Maintaining castrate status: Participants who have not undergone surgical orchiectomy should have received and continue on medical therapies, such as gonadotropin releasing hormone analogs, to maintain castrate levels of serum testosterone \<=50 ng/dL * Eastern Cooperative Oncology Group Performance Status of 0 to 2 * At least 4 weeks since an investigational agent prior to starting study therapy * At least 8 weeks since radioisotope therapy prior to starting study therapy * Recovery from any local therapy including surgery or radiation/radiotherapy for a minimum of 7 days prior to starting study therapy * Required initial laboratory values: white blood cell count \>=3,000/mm\^3; absolute neutrophil count \>=1,500/mm\^3; platelet count \>=100,000/mm\^3; creatinine level \<=1.5\*upper limit of normal (ULN); bilirubin \<=ULN; aspartate aminotransferase \<=2.5\*ULN; alanine aminotransferase \<=2.5\*ULN. Exclusion Criteria: * Symptomatic brain metastases or leptomeningeal metastases * Clinically significant cardiovascular disease, including myocardial infarction; ventricular tachyarrhythmia within 6 months; prolonged QTc \>450 msec; ejection fraction \<40%; or major conduction abnormality, unless a cardiac pacemaker is present * Pleural or pericardial effusion of any Common Terminology Criteria (CTC) grade * Peripheral neuropathy CTC Grade \>=2 * Currently active second malignancy other than nonmelanoma skin cancers. Participants are not considered to have a currently active malignancy if they have completed therapy and are now considered (by their physician) to be at less than 30% risk for relapse * Uncontrolled intercurrent illness including ongoing or active infection, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * HIV infection-positive patients receiving combination antiretroviral therapy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to the investigational agents * Receipt of any other investigational agents for the treatment of prostate cancer * Prior cytotoxic chemotherapy in the metastatic setting, with the exception of estramustine * Patients may continue on a daily multivitamin but must discontinue all other herbal, alternative, and food supplements before enrollment * Ketoconazole must be discontinued 4 weeks prior to starting study therapy * Antiandrogens must be discontinued prior to starting study therapy. Patients with a history of response to an antiandrogen and subsequent progression while on that antiandrogen should be assessed for antiandrogen withdrawal response for 4 weeks. Observation for antiandrogen withdrawal response is not necessary for those who have never responded to antiandrogens * Bisphosphonates must not be initiated within 28 days prior to starting study therapy * QT prolonging agents strongly associated with torsade de pointes.