Answer
$[0,3]\cup[5,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as
$x(x-3)(x-5)\geq0$
The boundary points are $x=0,3,5$
Step 2. Using test points to examine signs across the boundary points, we have
$...(-)...(0)...(+)...(3)...(-)...(5)...(+)...$
Thus the solutions are $0\leq x\leq 3$ plus $x\geq5$
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 $[0,3]\cup[5,\infty)$
