How Do You Solve sinx(sin x + 1) = 0 for All Solutions?

[xCanx]

I'm having trouble starting off with these equations:

sinx(sin x + 1) = 0

I can solve sin x + 1 =
Sin x = -1
x = -90

but then I don't know how to find all the solutions. Can someone please explain it to me. Thanks.

 

[Astronuc]

if h(x) = f(x)g(x), then h(x) = 0 if either f(x) = 0 or g(x) = 0, or f(x) = g(x) = 0, i.e. they have a common root.

Based on sinx (sin x + 1) = 0

one can have two possibilities: sin x = 0 and sin x = -1.

Consider if sin x = a, then x = sin^-1 (a), and remember that sin is a periodic function, i.e. sin x = sin (pi - x) and sin x = sin (x + 2pi).