There are several different techniques for factoring a second degree trinomial. One of the most commonly used is FOIL in reverse. It goes something like this.
Assume that (ax+b)(cx+d) = 3x[sup:1j1ih1ra]2[/sup:1j1ih1ra]-20x-63
You have to find a, b, c and d such that....
1) ac = 3.
2) ad + bc = -20
and
3) bd = -63.
From 1) we know that either a=1 and c=3 or a=3 and c=1.
From 3) we have these possibilities.
b=1 and d=-63 or b=-63 and d=1
b=3 and d=-21 or b=-21 and d=3
b=7 and d=-9 or b=-9 and d=7.
I can't think of any other possibilities.
Now, you have to make the choices so that ad + bc = -20.