How do you factor without a computer? (Obviously, I used a computer).
Are you aware of the Rational Root Theorem?
For convenience I'm going to divide the polynomial by 6:
Possible rational roots to this polynomial equation are:
That gives you 12 possible rational roots that you can check.
If you don't know that one, then you're probably stuck with Cardano's method. (Cardano's method is about 1/2 way down the page.)
-Dan