In this study, our main goal is to study the combination of docetaxel + carboplatin and vandetanib, followed by a double-blind randomized assignment to maintenance therapy with vandetanib 300 milligrams (mg) or placebo by mouth daily until disease progression to determine if maintenance therapy can prolong progression-free survival. In addition to clinical efficacy outcomes we will monitor for safety and tolerability, as well as explore any differences in outcome based on age and gender.