I need to solve this equation (3 sin x + 4 cos x)^2 = 3^2.

I have solved this far, and it doesn't seem that I'm getting anywhere to the solution.

9 sin^2 x + 24 sin x cos x + 16 cos^2 x = 9

9 sin^2 x + 12 sin 2x + 16 cos^2 x = 9

9 sin^2 x + 12 sin 2x + 16(1 - sin^2 x) = 9

9 sin^2 x + 12 sin 2x + 16 - 16 sin^2 x = 9

- 7 sin^2 x + 12 sin 2x = -7

Where do I go from here?! It doesn't look I can factorise...