Answer
$(-1,0)U(3,\infty)$
Work Step by Step
Step 1.Factor and identify boundary points (zeros) $x(x+1)(x-3)\gt0$ as $x=-1,0,3$ which divide the x-axis into four intervals $(-\infty,-1),(-1,0),(0,3),(3,\infty)$
Step 2. Choose test values in each interval $x=-2,-0.5,1,4$ and test the inequality to get $False,\ True, \ False, \ True$
Step 3. Thus the solution intervals are $(-1,0)U(3,\infty)$