which are the solutions of sin2x = 2sinx?

First, we'll substitute sin 2x by the equivalent expression 2sin x*cosx 

2 sin x*cos x= 2sin x

We'll move all terms to one side:

2 sin x*cos x - 2 sin x=0

2 sin x (cos x -1)=0

We'll put each factor from the product above as being 0.

2 sin x =0

We'll divide by 2:

sin x=0

This is an elementary equation:

x = arcsin 0

x=0 or x=pi

cos x - 1=0

This is an elementary equation, also:

cos x=1

x=+/-arccos 1

x=0, x=pi

The solutions of the equation are {0,pi}.