X^2 - 4x - 12 = 0 Factor and solve

Ax^2+bx+c=0

find what 2 numbers multiply to get c and add to get b
x^2-4x-12
b=-4
c=-12

x times y=-12
x+y=-4
factor -12
-1, 12
-2,6
-3,4
add
-1+12=11
-2+6=4
-3+4=1

the one that works is -2 and 6 because they can be reversed to make -6 and 2 which multiploy to get -12 and add to get -4 so 

split it up into

x^2-4x-12=(x-6)(x+2)=0
set each to zero
x-6=0
add 6
x=6

x+2=0
subtract 2
x=-2

x=6 or -2