We recognise the left hand side to be in the form:

sin(a − b) = sin a cos b − cos a sin b,

where a = 2x and b = x.

So

sin 2x cos x − cos 2x sin x

= sin(2x − x)

= sin x

Now, we know the solutions of sin x = 0 to be:

x = 0, π.

[Why?]