$\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$
$\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$