Inclusion Criteria: - Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. - Histological or cytological confirmed diagnosis of a solid tumor. In the dose escalation phase, the tumor must be unresectable and locally advanced, or metastatic, and either no proven effective therapy exists or the patient cannot tolerate such therapy. Patients enrolled in the expanded MTD phase of the study must have either HCC or another select tumor type (melanoma, head and neck, colorectal, breast, or thyroid). For HCC patients in the expanded MTD phase: - Documentation of original biopsy for diagnosis is acceptable if tumor tissue is unavailable. Histological confirmation is mandatory for patients without cirrhosis. - Patients with cirrhosis may have a clinical diagnosis of HCC by the American Association for the Study of Liver Diseases (AASLD) criteria.-cytotoxic chemotherapy; a targeted agent, including sorafenib; or other experimental treatment) are eligible. For non-HCC patients in the expanded MTD phase: - The tumor must be amenable to biopsy and the patient must be willing to consent to biopsy. - Life expectancy of > 3 months. - Evidence of measurable disease by RECIST criteria on computer assisted tomography (CT) or magnetic resonance imaging (MRI). - Normal/adequate swallowing capability, functional small bowel intact, and no malabsorption problems (in order to maximally quantify PK absorption characteristics). - Amylase and lipase < or equal to 2 x upper limit of normal (ULN). - Hemoglobin > or equal to 8.5 g/L. - ANC > or equal to 1,500/mm3. - Platelet count > or equal to 75,000/mm3. - Total bilirubin < or equal to 1.5 x ULN (For patients with HCC, refer to criterion number 14). - Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) < or equal to 2.5 x ULN (< or equal to 5 x ULN for patients with liver involvement). - PT-INR/PTT < or equal to 1.5 x ULN (Patients who are being prophylactically anti-coagulated with an agent such as coumadin or low molecular weight heparin (LMWH) or therapeutically anti-coagulated with LMWH will be allowed to participate provided that they meet these criteria; in addition, these patients must be monitored at appropriate intervals throughout the study). - Patients with HCC should have a Child-Pugh score of 5-6 (Class A). - Creatinine < or equal to 1.5 x ULN. - Patients must not be pregnant or breast-feeding, as chemotherapy is thought to present substantial risk to the fetus/infant. Men and women of reproductive potential may not participate in this study unless they have agreed to use an effective contraceptive method while on study. - No severe or uncontrolled intercurrent illness that in the opinion of the investigator would adversely impact the safety or efficacy of the treatment. - Ability to understand and willingness to sign a written informed consent form. - Patients must be within normal range cardiac function as measured by echocardiogram or multiple-gated acquisition (MUGA) scan. Exclusion Criteria: - Previous treatment with sorafenib that required a dose reduction due to toxicity. - Previous treatment with RDEA119. - Patients who have had cytotoxic chemotherapy or radiotherapy within 4 weeks prior to entering the study, those who have not recovered from adverse events due to agents administered more than 4 weeks earlier, those who have concurrent use of cytotoxic chemotherapy not indicated in the study protocol, or those with use of any other investigational agents < 4 weeks from the first dose of the study drug. - Previous or concurrent cancer that is distinct in primary site or histology from the cancer being evaluated in the study except cervical carcinoma in situ, treated basal cell carcinoma, superficial bladder tumors [Ta, Tis & T1] or any cancer curatively treated > 3 years prior to study entry. - Swallowing dysfunction and/or malabsorption syndrome that would impair sorafenib and RDEA119 treatment. - Cardiac disease: Congestive heart failure > New York Heart Association (NYHA) Class 2. Patients must not have unstable angina or new onset angina (within the last 3 months) or myocardial infarction (MI) within the past 6 months. - Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. - Uncontrolled hypertension - Known human immunodeficiency virus (HIV) infection. - Thrombotic or embolic events such as cerebrovascular accident including transient ischemic attacks within the past 6 months. - Evidence or history of bleeding diathesis or coagulopathy. - Major surgery, open biopsy or significant traumatic injury within 4 weeks of first dose of study drug. - The use of inhibitors or inducers of CYP3A4 and CYP2C19 enzymes, as well as the concurrent treatment with any of the agents listed in Section 3.7 of the protocol. These and other medications that are inhibitors and inducers of CYP3A4 and CYP2C19 should be discussed with the sponsor. - Patients with known hypersensitivity to any of the drugs or components given in this protocol. - Patients with abdominal fistula, gastrointestinal (GI) perforation, intra-abdominal abscess, or small bowel resection, any of which is within 6 months of study entry. - Patients with abdominal radiation resulting in chronic diarrhea. - Patients with documented central nervous system (CNS) metastasis who are not off steroids and other CNS therapies. - Evidence of uncontrolled active infections except HCV and HBV. - Other serious medical or psychiatric illness that would not permit the patient to be managed according to the protocol.