Answer
$(-3,0)\cup(1,\infty)$
Work Step by Step
Step 1. Rewriting and factor the inequality as $x^3+2x^2-3x=x(x^2+2x-3)=x(x+3)(x-1)\gt0$, we can identify the boundary points as $x=-3,0,1$
Step 2. Use test points to examine the signs of the left side across the boundary points; we have $...(-)...(-3)...(+)...(0)...(-)...(1)...(+)...$; thus the solutions are $(-3,0)\cup(1,\infty)$
Step 3. We can graph the solution on a real number line as shown in the figure.
