finish up in WordNet English dictionary

1. finish a task completely
   "I finally got through this homework assignment"
   get through  wrap up  finish off  mop up  polish off  clear up  finish up 
   
2. finally be or do something
   "He ended up marrying his high school sweetheart"; "he wound up being unemployed and living at home again"
   finish up  land up  fetch up  end up  wind up  finish