To solve the equation 6(x+2)(x-3)-3(x-2)^(2)-3(x-1)(x+1)=1, we can start by expanding and simplifying each term:

6(x+2)(x-3) = 6(x^2 - x - 6) = 6x^2 - 6x - 36

-3(x-2)^(2) = -3(x^2 - 4x + 4) = -3x^2 + 12x - 12

-3(x-1)(x+1) = -3(x^2 - 1) = -3x^2 + 3

Now, we can substitute these simplified expressions back into the original equation:

6x^2 - 6x - 36 - 3x^2 + 12x - 12 - 3x^2 + 3 = 1

Combining like terms:

(6x^2 - 3x^2 - 3x^2) + (-6x + 12x) + (-36 - 12 + 3) = 1

0x^2 + 3x + -45 = 1

Simplifying further:

3x - 42 = 1

Adding 42 to both sides:

3x = 43

Dividing both sides by 3:

x = 43/3

Therefore, the solution to the equation is x = 43/3.