Factor the quadratic equations W^2-W-12

Given

W^2-W-12 = w^2+bW+c

b=-1,

c=-12

We look for m, n so that m+n=b=-1, m*n=c=-12, where m, n are integer factors of - 12.

Now enumerate all possibilities for m*n=12

m n m*n m+n

1 - 12 - 12 - 11

2 - 6 - 12 - 4

3 - 4 - 12 - 1 ... so m*n=-12, m+n=-1

The factorization is then

W^2-W-12 = (W+3) (W-4)