what was the equation you got? show us and we'll take it from there, there is no one way to attack a quartic, we must do it by case

EDIT: ok, this is not a "nice" quadratic, it does not have integer roots. so if you have to solve this by hand i see no other way to do it at the moment other than to use the quartic formula. which is a mess. you can use Cardano's or Galois' method (your professor is cruel)