To solve for x, we can first rewrite the equation using the cosine double angle identity:

3sinx*cosx = sin2x

Now our equation becomes:

sin2x + cos^2x = 0

Using the Pythagorean identity sin^2x + cos^2x = 1, we can substitute sin^2x = 1 - cos^2x into the equation:

1 - cos^2x + cos^2x = 0
1 = 0

This equation has no solution, which means the original equation 1-3sinx*cosx+cos^2x=0 also has no solution.