2sin2(x)+3sin(x)+1=0=(2sin(x)+1)(sin(x)+1).
Therefore sin(x)=-½ or -1.
So x=-π/6, -5π/6 or -π/2. To make these more general we need to add 2nπ where n is any integer.
When n=1: x=11π/6, 7π/6, or 3π/2. When n=2: x=23π/6, 19π/6, 7π/2, etc.
To convert to degrees, substitute π=180°, which makes π/6=30°.