Given equation is 15^(2x-3) = 3^x * 5^(3x-6).

Now we can rewrite 15 as 3 * 5, so the equation becomes:

(3 5)^(2x-3) = 3^x 5^(3x-6)

Expanding the left side using the properties of exponents, we get:

3^(2x-3) 5^(2x-3) = 3^x 5^(3x-6)

Now we can separate the exponents to get:

3^(2x) 3^(-3) 5^(2x) 5^(-3) = 3^x 5^(3x-6)

Rearranging the terms, we get:

3^(2x) 5^(2x) = 3^(x+3) 5^(3x-6)

Now we can equate the exponents to solve for x:

2x = x + 3
x = 3

Therefore, the solution to the given equation is x = 3.