2cos²(x)=3sin(x)+3, 2(1-sin²(x))=3sin(x)+3, 2-2sin²(x)=3sin(x)+3, 2sin²(x)+3sin(x)+1=0 is a quadratic that can be factorised: (2sin(x)+1)(sin(x)+1)=0. Therefore, sin(x)=-½ or sin(x)=-1.
We can give the answers in degrees or radians.
Degrees: x=-30°, which is 360-30=330°. Also 180+30=210°. But we can also have angles bigger than 360°, so other solutions are 360+210=570°, 360+330=690°. We can write the general answers as 210+360n and 330+360n where n is any integer. When sin(x)=-1 we have x=-90°, which is the same as 360-90=270° and 270+360n.
Radians: 30° is π/6 radians because 180° is π radians (about 3.14). -30°=-π/6=2π-π/6=11π/6 and π+π/6=7π/6. So the answers are 7π/6+2πn, 11π/6+2πn, 3π/2+2πn.