Solve: $3\sin{2x}+4\cos{2x}-2\cos{x}+6\sin{x}-6=0$ 
Solve:   $3\sin{2x}+4\cos{2x}-2\cos{x}+6\sin{x}-6=0$

My Try
$6\sin{x}\cos{x}+4(\cos^2{x}-\sin^2{x})-2\cos{x}+6\sin{x}-6=0$
I have expanded the equation, But I cannot proceed further, Any hint would be appreciated. Thank you!

$x=2y$  we get after some manipulation $$-4\cos^4 y-36\cos^2y\sin^2 y+24\cos^3 y\sin y=0$$ $$-4\cos^2 y{(\cos y-3\sin y)}^2=0$$ can you end it??
