Solve:

6sin square x - sinxcosx - cos square x =3

use cos^2(x) =(1+cos2x)/2 sin^2(x) =(1-cos2x)/2 and sinxcosx = sin(2x)/2, solve the resulting equation for 2x and then divide by 2 to get x

6sin²x-sinx.cosx-cos²x = 3

multiplying 2 on both sides we get

12sin²x-2sinx.cosx-2cos²x = 6

but we know that cos²x=1-sin²x  and  2sinx.cosx=sin2x

12sin²x-sin2x-2(1-sin²x) = 6

12sin²x-sin2x-2+2sin²x = 6

14sin²x-sin2x = 6+2 = 8

further simplify