$\sin 2x-\cos 2x -3 \sin x-\cos x+2=0$
$\Leftrightarrow (2\sin x.\cos x-\cos x)-1+2\sin^2 x-3\sin x+2=0$
$\Leftrightarrow \cos x(2\sin x-1)+(2\sin^2 x-3\sin x+1)=0$
$\Leftrightarrow \cos x(2\sin x-1)+(2\sin x-1)(\sin x-1)=0$
$\Leftrightarrow (2\sin x-1)(\cos x-\sin x-1)=0$