To solve the equation 4/(x-3) + 15/(x+3) = 18/x, we need to find a common denominator for all three terms. The least common denominator is (x-3)(x+3)(x).

Multiplying each term by the common denominator, we get:

4(x)(x+3) + 15(x-3) = 18(x-3)(x+3)

Expanding both sides of the equation, we get:

4x^2 + 12x + 15x - 45 = 18x^2 - 54

Combining like terms:

4x^2 + 27x - 45 = 18x^2 - 54

Rearranging terms:

14x^2 - 27x + 9 = 0

Now, we can solve the quadratic equation using the quadratic formula:

x = [-(-27) ± √((-27)^2 - 4149)] / 2*14
x = [27 ± √(729 - 504)] / 28
x = [27 ± √225] / 28
x = [27 ± 15] / 28

The possible solutions are:
x = (27 + 15) / 28 = 42/28 = 3/2
x = (27 - 15) / 28 = 12/28 = 3/7

Therefore, the solutions to the equation 4/(x-3) + 15/(x+3) = 18/x are x = 3/2 and x = 3/7.