Answer
$(-\infty,-5) $.
Work Step by Step
Step 1. For $3x^3+15x^2\lt0 \Longrightarrow 3x^2(x+5)\lt0$, identify boundary points as $x=-5,0$.
Step 2. Form intervals $(-\infty,-5),(-5,0),(0,\infty)$.
Step 3. Choose test values for each interval $x=-6,-1,1$.
Step 4. Test the inequality to get results: $True,\ False,\ False$
Step 5. We have the solution $(-\infty,-5) $.
