Answer
$\pi,\frac{\pi}{3},\frac{5\pi}{3}$
Work Step by Step
1. Treat $cos(x)$ as a single unit, we have $(2cos(x)-1)(cos(x)+1)=0$, thus $cos(x)=-1, \frac{1}{2}$
2. For $cos(x)=-1$, we have $x=\pi$ within $[0,2\pi)$,
3. For $cos(x)=\frac{1}{2}$, we have $x=\frac{\pi}{3},\frac{5\pi}{3}$ within $[0,2\pi)$,
