First, expand the expression:

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

Now the equation becomes:

2x^2 - 2 - (x+1) - 12 = 0
2x^2 - 2 - x - 1 - 12 = 0
2x^2 - x - 15 = 0

Now we have a quadratic equation in the form of ax^2 + bx + c = 0:

a = 2, b = -1, c = -15

To solve for x, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

Substitute the values of a, b, and c into the formula:

x = (1 ± √((-1)^2 - 4 2 -15)) / 2 * 2
x = (1 ± √(1 + 120)) / 4
x = (1 ± √121) / 4

Now simplify:

x = (1 ± 11) / 4

This gives us two possible solutions:

x = (1 + 11) / 4 = 12 / 4 = 3
x = (1 - 11) / 4 = -10 / 4 = -2.5

So the solutions to the equation 2(x-1)(x+1)-(x+1)-12=0 are x = 3 and x = -2.5.