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!

$6\sin{x}\cos{x}+4(\cos^2{x}-\sin^2{x})-2\cos{x}+6\sin{x}-6=0$
$6\sin{x}\cos{x} -9\sin^2{x} - \cos^2{x} -2\cos{x} + 6\sin{x} - 1=0$
$-(3 \sin x - \cos x)^2 + 2(3 \sin x - \cos x) - 1= 0$
$(3 \sin x - \cos x)^2 - 2(3 \sin x - \cos x) + 1= 0$
