Answer
$(-3,4)$
Work Step by Step
Step 1. Rewrite the inequality as
$x^2-x-12=(x-4)(x+3)\lt0$
Thus the boundary points are $x=-3,4$
Step 2. Using test points to examine the signs of the left side across the boundary points, we have $...(+)...(-3)...(-)...(4)...(+)...$; thus the solutions are $(-3,4)$
Step 3. We can graph the above solution on a real number line as shown.
