Answer
$\{-2\}\cup[2,\infty)$
Work Step by Step
Step 1. Factor the inequality as
$x^2(x+2)-4(x+2)\geq0$
or
$(x+2)^2(x-2)\geq0$
The boundary points are $x=-2,2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(-)...(-2)...(-)...(2)...(+)...$
Thus the solutions are:
$x\geq2$ plus $x=-2$
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 $\{-2\}\cup[2,\infty)$
