To simplify the given expression:

3sin^2(x) + 5cos^2(x) - 2cos(2x) + 4sin2x = 0

We can use the trigonometric identity: cos(2x) = cos^2(x) - sin^2(x)

Now, substituting that identity into the original equation, we get:

3sin^2(x) + 5cos^2(x) - 2(cos^2(x) - sin^2(x)) + 4sin(2x) = 0

Now, simplify the equation:

3sin^2(x) + 5cos^2(x) - 2cos^2(x) + 2sin^2(x) + 4sin(2x) = 0

This simplifies to:

5sin^2(x) + 3cos^2(x) + 4sin(2x) = 0

There isn't a direct way to further simplify this expression since it involves both sine and cosine functions.