Resolve $\cos(3x)= \cos(2x)$
Notice, we have $$\cos(3x)=\cos(2x)$$ $$3x=2n\pi\pm 2x$$ Where, $n$ is any integer
Now, we have the following solutions
$$3x=2n\pi+2x\implies \color{red}{x=2n\pi}$$ or $$3x=2n\pi-2x\implies \color{red}{x=\frac{2n\pi}{5}}$$
We have the formula $$ \cos{(a+b)}-\cos{(a-b)} = -2\sin{a}\sin{b}, $$ so if we put $a=5x/2,b=x/2$, we have $$ 0 = \cos{3x}-\cos{2x} = -2\sin{\left(\frac{5}{2}x\right)}\sin{\left(\frac{x}{2}\right)},$$ so you just have to determine the $x$ for which either one of the sines is equal to $0$, which I'm sure you can do.