Answer
$(-4,0)U(0,\infty)$
Work Step by Step
Step 1. Factor and identify boundary points (zeros) $2x^2(x+4)\gt0$ as $x=-4,0$ which divide the x-axis into three intervals $(-\infty,-4),(-4,0),(0,\infty)$
Step 2. Choose test values in each interval $x=-5,-1,1$ and test the inequality to get $False,\ True,\ True$
Step 3. Thus the solution interval is $(-4,0)U(0,\infty)$
