This study is for patients who have been diagnosed with advanced solid tumors or ALK+ Non-Small Cell Lung Cancer and standard drugs are no longer effective or there is not an effective treatment known for a patient's type of cancer. The investigational drug in this study is X-396. X-396 has not been given to humans before this study. The purpose of this study is to evaluate the safety of an investigational drug, X-396, and to determine the best dose to use for future studies. Participants can expect to be in this study for up to 60 months, but may withdraw from the study once they no longer experience benefit from the study.