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)