<s>[INST] Solving $\sin^2x + 3\sin x\cos x + 2\cos^2x=0$, for $0\leq x\leq 2\pi$ 
Solve
$$\sin^2x + 3\sin x\cos x + 2\cos^2x=0$$
for $0\leq x\leq 2\pi$.

My answers are
$$x=2.03, 5.18 \qquad\text{or}\qquad
x=\frac{3\pi}{4},\frac{7\pi}{4} \qquad\text{or}\qquad
x=\frac{\pi}{2}, \frac{3\pi}{2},$$
but the answer states $x=2.03, 5.18$ or $x=3\pi/4,7\pi/4$ only.
I got $x=\pi/2, 3\pi/2$ from $(\cos x)^2=0$,
where it is a factor in one of my steps:
$$\cos^2x\left(\tan^2x+3\tan x+2\right)=0.$$
 [/INST] Look at this $$x^2+3xy+2y^2=(x+y)(x+2y)$$ can you see??
</s>