Answer
$\{\frac{3\pi}{4}, 2.1588, \frac{7\pi}{4}, 5.3004 \}$
Work Step by Step
Step 1. Factor the equation as $(2tan(x)+3)(tan(x)+1)=0$; thus $tan(x)=-1$ and $tan(x)=-1.5$
Step 2. For $tan(x)=-1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{3\pi}{4},\frac{7\pi}{4}$
Step 3. For $tan(x)=-1.5$, we can find the reference angle as $x_0=tan^{-1}(1.5)\approx0.9828$ and all x-values in $[0,2\pi)$ as $x=\pi-x_0\approx2.1588$ and $x=2\pi-x_0\approx5.3004$
Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{3\pi}{4}, 2.1588, \frac{7\pi}{4}, 5.3004 \}$
