Answer
$\frac{7\pi}{18},\frac{11\pi}{18},\frac{19\pi}{18},\frac{23\pi}{18},\frac{31\pi}{18},\frac{35\pi}{18}$
Work Step by Step
Step 1. Given the equation $sin(3x)=-\frac{1}{2}$, we can write the general solutions as $3x=2k\pi-\frac{\pi}{6}$ and $3x=2k\pi-\frac{5\pi}{6}$, where $k$ is an integer. Thus
$x=\frac{2k\pi}{3}-\frac{\pi}{18}$ and $x=\frac{2k\pi}{3}-\frac{5\pi}{18}$
Step 2. We are restricted to find $x\in[0,2\pi)$, by testing $k$ values, we can find
$x=\frac{7\pi}{18},\frac{11\pi}{18},\frac{19\pi}{18},\frac{23\pi}{18},\frac{31\pi}{18},\frac{35\pi}{18}$
