Answer
$[-4,-3]U[3,\infty)$
Work Step by Step
Step 1. Rewrite and factor to get $x^2(x+4)-9(x+4)\ge0$ or $(x+4)(x+3)(x-3)\ge0$. Identify the boundary point at $x=-4,-3,3$
Step 2. Plot the above points on a number line and obtain four intervals $(-\infty,-4],[-4,-3],[-3,3],[3,\infty)$
Step 3. Choose test values at $x=-5,-3.5,0,4$ for each interval and test the inequality. The results are $F,T,F,T$ (T for True, F for False) for each interval.
Step 4. The solutions are the intervals with true results: $[-4,-3]U[3,\infty)$
