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]