Answer
$[-2,-1]\cup[1,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as
$x^2(x+2)-(x+2)\geq0$
or
$(x+2)(x+1)(x-1)\geq0$
The boundary points are $x=-2,-1,1$
Step 2. Using test points to examine signs across the boundary points, we have
$...(-)...(-2)...(+)...(-1)...(-)...(1)...(+)...$
Thus the solutions are $-2\leq x\leq -1$ plus $x\geq1$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $[-2,-1]\cup[1,\infty)$
