Answer
$ (-3,0)\cup(1,\infty)$.
Work Step by Step
Step 1. For $x^3+2x^2-3x\gt0 \Longrightarrow x(x-1)(x+3)\gt0$, identify boundary points as $x=-3,0,1$.
Step 2. Form intervals $(-\infty,-3),(-3,0),(0,1),(1,\infty)$.
Step 3. Choose test values for each interval $x=-4,-1,0.5,2 $.
Step 4. Test the inequality to get results: $False,\ True,\ False,\ True$
Step 5. We have the solution $ (-3,0)\cup(1,\infty)$.
