To simplify this equation we need to use the trigonometric identity: sin^2(x) + cos^2(x) = 1

Given equation: 3sin^2(x) + 4cos^2(x) = 6.5sin(2x)

Rewriting sin(2x) as 2sin(x)cos(x), we get:
3sin^2(x) + 4cos^2(x) = 13sin(x)cos(x)

Using the trigonometric identity: sin^2(x) + cos^2(x) = 1, we can replace sin^2(x) and cos^2(x) in terms of sin(x) and cos(x):
3(1 - cos^2(x)) + 4cos^2(x) = 13sin(x)cos(x)
3 - 3cos^2(x) + 4cos^2(x) = 13sin(x)cos(x)
3 + cos^2(x) = 13sin(x)cos(x)

Since we have reached this form, the equation does not have a simple simplified form and remains as:
3 + cos^2(x) = 13sin(x)cos(x)