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)