Need help understanding the process to solve sin^2x-cos(2x)= (-1/4)

Question

Solve:       sin^2x - cos(2x) = (- 1/4)     exactly on     0<= x < 2pi

need help with step by step in order to solve. I'm having trouble with getting past what to do after
replacing cos(2x) with an identity. Or maybe I'm just doing this all wrong. If anyone can walk me through
each step in simple terms that would be awesome. I have many more like this one to solve and I'd like
to understand the process better. Thank you in advance.

Answer 1

Replace cos(2x) with 1-2sin^2(x) so that we have an equation with sine only.

sin^2(x)-1+2sin^2(x)=-(1/4); 3sin^2(x)=1-(1/4)=3/4; sin^2(x)=1/4 (dividing through by 3); sin(x)=+1/2 so x=(pi)/6, 5(pi)/6, 7(pi)/6, 11(pi)/6 or 30, 150, 210, 330 degrees.