To solve the equation sin(6x)sin(2x) = sin(3x)sin(5x), we can use the trigonometric identity sin(A)sin(B) = 0.5[cos(A - B) - cos(A + B)].

First, let's rewrite the equation:

0.5[cos(6x - 2x) - cos(6x + 2x)] = 0.5[cos(3x - 5x) - cos(3x + 5x)]

Simplify both sides:

0.5[cos(4x) - cos(8x)] = 0.5[cos(-2x) - cos(8x)]

Now, simplify further:

0.5cos(4x) - 0.5cos(8x) = 0.5cos(-2x) - 0.5cos(8x)

0.5cos(4x) = 0.5cos(-2x)

Since cos(-2x) = cos(2x), we can simplify further:

cos(4x) = cos(2x)

Now, we know that cos(A) = cos(B) if A = B or A = -B + 2nπ, where n is an integer.

So, solve for x:

4x = 2x + 2nπ
2x = 2nπ
x = nπ

Therefore, the solutions to the equation sin(6x)sin(2x) = sin(3x)sin(5x) are x = nπ, where n is an integer.