Question

Find all solutions to the equation.

sin2x + sin x = 0

Answer 1

2sin(x)cos(x)+sin(x)=0
sin(x)[2cos(x)+1]=0
either sin(x)=0 x=n*pi
or cos(x)=-1/2 x=2n*pi+ pi/6 , 2n*pi -pi/6

Answer 2

Or, if you mean
\[\sin^2x+\sin x=0\\
\sin x\left(\sin x+1\right)=0\]
Then you have
\[\begin{matrix}\sin x=0&&&\sin x=-1\\
x=2n\pi&&&x=\frac{3\pi}{2}+2n\pi\end{matrix}\]