X^2-4x-12>0
First we will solve the inequality just like we solve any quadric equation.
x^2-4x-12>0
(x-6)(x+2)>0
That means that both terms are either negative or both positive: OR
(x-6)>0 and (x+2)>0
x>6 and x>-2
==> the x belongs to the interval (6, inf)
OR
(x-6)<0 and (x+2)<0
x<6 and x<-2
Then x belongs to the interval (-inf, -2)
From both solution we observe that x belongs to R except for the interval [-2,6]
then x = R-[-2,6]