Answer
$ (-1,0)\cup(3,\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 $x=-1,0,3$.
Step 2. Form intervals $(-\infty,-1),(-1,0),(0,3),(3,\infty)$.
Step 3. Choose test values for each interval $x=-2,-0.5,1,4$.
Step 4. Test the inequality to get results: $False,\ True,\ False,\ True$
Step 5. We have the solution $ (-1,0)\cup(3,\infty)$.
