This partially randomized phase I trial studies the side effects and how well sequential dosing of vascular endothelial growth factor receptor (VEGFR)/platelet derived growth factor receptor (PDGFR) dual kinase inhibitor X-82 and docetaxel works in treating patients with solid tumors. VEGFR/PDGFR dual kinase inhibitor X-82 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as docetaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving VEGFR/PDGFR dual kinase inhibitor X-82 and docetaxel one at a time instead of concurrently may work in treating patients with solid tumors.