To solve this equation, we need to find a common denominator for all the terms. The common denominator is (x^2-36)(36-12x+x^2)(2x+12).

Rewriting each term with the common denominator:

(6/(x^2-36)) ((36-12x+x^2)(2x+12)/(36-12x+x^2)(2x+12)) + (1/(36-12x+x^2)) ((x^2-36)(2x+12)/ (x^2-36)(2x+12)) + (1/(2x+12)) * ((x^2-36)(36-12x+x^2) / (x^2-36)(36-12x+x^2))

This simplifies to:

6(36-12x+x^2)(2x+12) + (x^2-36)(2x+12) + (x^2-36)(36-12x+x^2) = 0

Expanding and simplifying:

432x + 216 - 144x + 6x^2 + 3x^3 - 72 - 36x - 6x^2 - 216 + 432x - 1296 + 36x^2 = 0

Combining like terms:

3x^3 + 36x^2 - 36x = 0

Dividing by 3:

x^3 + 12x^2 - 12x = 0

Factoring out x:

x(x^2 + 12x - 12) = 0

Now, we solve for x by setting each factor to zero:

1) x = 0

2) x^2 + 12x - 12 = 0

Using the quadratic formula, we find the roots of the equation x^2 + 12x - 12 = 0:

x = (-b ± √(b^2 - 4ac)) / 2a
x = (-12 ± √(144 + 48)) / 2
x = (-12 ± √192) / 2
x = (-12 ± 8√3) / 2
x = -6 ± 4√3

Therefore, the solutions to the given equation are x = 0, x = -6 + 4√3, and x = -6 - 4√3.