A trigonometry equation: $3 \sin^2 \theta + 5 \sin \theta \cos \theta - 2\cos^2 \theta = 0$ 
$$3 \sin^2 \theta + 5 \sin \theta \cos \theta - 2\cos^2 \theta = 0$$

What are the steps to solve this equation for $ \theta $?
Because, I  am always unable to deal with the product $\sin \theta \cos \theta$.

Following excellent advice by @raul, you write immediately
$$\tan(\theta)=\frac{-5\pm\sqrt{5^2+4\cdot3\cdot2}}{2\cdot3}=\frac13,-2.$$
