Answer
$x=n\pi$,
$x=\frac{\pi}{3}+2n\pi$ and
$x=\frac{5\pi}{3}+2n\pi$
Work Step by Step
$sin~2x-sin~x=0$
$2~sin~x~cos~x-sin~x=0$
$sin~x~(2~cos~x-1)=0$
$sin~x=0$ or $cos~x=\frac{1}{2}$
The solutions in $[0,2\pi)$ are:
$x=0$, $x=\frac{\pi}{3}$, $x=\pi$ and $x=\frac{5\pi}{3}$
General solution:
$x=2n\pi$,
$x=\frac{\pi}{3}+2n\pi$,
$x=\pi+2n\pi$ and
$x=\frac{5\pi}{3}+2n\pi$
or
$x=n\pi$,
$x=\frac{\pi}{3}+2n\pi$ and
$x=\frac{5\pi}{3}+2n\pi$
