Solve for x (x+1)(x-3)>12

There are three important numbers coming from the factors, 0, -1, and 3 test using numbers around those numbers.

Using -2 because it is less than -1
(-2)(-2+1)(-2-3) =-10 which is < 12
Using -.5 because it is between -1 and 0
(-.5)(-.5+1)(-.5-3)=.875 which is <12
Using 1 because it is between 0 and 3
1(1+1)(1-3)=-4 < 12
Using 4 because it is greater than 3
4(4+1)(4-3)=20 > 12
Therefore x>4 for x(x+1)(x-3)>12
also you can look at the graph