Answer
$(-4,0)\cup(0,\infty)$.
Work Step by Step
Step 1. For $2x^3+8x^2\gt0 \Longrightarrow 2x^2(x+4)\gt0$, identify boundary points as $x=-4,0$.
Step 2. Form intervals $(-\infty,-4),(-4,0),(0,\infty)$.
Step 3. Choose test values for each interval $x=-5,-1,1$.
Step 4. Test the inequality to get results: $\ False,\ True,\ True$
Step 5. We have the solution $(-4,0)\cup(0,\infty)$.
