trigonometry - Trigonometric equation cos sin and power

The problem is $2\cos t - 3\sin^2t +2 = 0$.
I get to $2\cos t -3\sin^2t =-2$
I think that I need to use a trigonometric identity like $\cos(x+y)$ and to divide $2\cos t -3\sin^2t$ with the $\sqrt{2^2+3^2}$

Do you know how to solve this? It should be $\sqrt{2^2 + 3^2}$

Answer

$$2 \cos t - 3 \sin^2t +2 = 0\\.$$ Write $$\sin^2 t=1-\cos^2 t,$$ then you have a quadratic equation. Solve for $\cos t$ $$2\cos t -3(1-\cos^2 t)+2=0\\3\cos ^2 t+2\cos t-3+2=0\\\cos t=-1,\;\frac{1}{3}.$$