x^3-144x<0 .....let's factor the left side as
x(x -144) < 0 = x( x + 12) (x - 12) < 0
The solution comes from one, or more, of these intervals :
(-inf, -12) (-12, 0) (0, 12) (12, inf)
If we pick the test points, - 13, -3, 3, and 13 and put them in the factored equation, -3 and 13 make the inequality true, but -13 and 3 make it false
So.....the solution intervals are (-12, 0) and (12, inf)
Here's a graph that will show this is true : https://www.desmos.com/calculator/uc5lu7mmsj