1. The problem statement, all variables and given/known data

sin6x+sin4x=0

2. Relevant equations

sinx=2sin\frac{x}{2}cos\frac{x}{2}

sin2x=2sinxcosx

cos2x=cos^2x-sin^x

3. The attempt at a solution

2sin3xcos3x+2sin2xcos2x=0

sin3xcos3x+sin2xcos2x=0

What shall I do next?

What are you trying to do? Solve for x?

Also, you might want to use something like:

\sin(a+b) = \sin a \cos b + \cos a \sin b