Generally the way you solve it is find all rational roots. You should have learned how to find all candidates for rational roots already, by looking at the leading coefficient and the constant term. Test each. When you've found one, call it a, synthetically divide the polynomial by (x-a). Repeat the process until you've found all rational roots. At this point you should be able to take the remaining polynomial and either factor it or use the quadratic to find any remaining roots.