trigonometry - solving Trigonometric equations: $textrm{cos}(5x)textrm{cos}(x)=textrm{sin}(5x)textrm{sin}(x)-0.5$

Question: Find solutions for $\textrm{cos}(5x)\textrm{cos}(x)=\textrm{sin}(5x)\textrm{sin}(x)-0.5$

I did $\textrm{cos}(6x)=-1/2$ using the subtraction formula for cos.
I'm confused how to find the solutions now since there are 12.

I thought you could just see that its $\cos$ of 20 degrees and see what solutions are in quadrant 1 and 4, but do you add the period to get the 12 solutions? If someone could explain how to find the twelve solutions that would be great.