Let's first simplify the left side of the equation before solving for x.

Expanding each term:

6(x+1)^2 = 6(x^2 + 2x + 1) = 6x^2 + 12x + 6

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

Expanding (x+1)^3:

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

Now substitute these expanded terms back into the equation and simplify:

6x^2 + 12x + 6 + 2(x^3 + 1) - 2(x^3 + 3x^2 + 3x + 1) = 26

6x^2 + 12x + 6 + 2x^3 + 2 - 2x^3 - 6x^2 - 6x - 2 = 26

Collect like terms:

12x - 6 = 26

12x = 32

x = 32/12

x = 8/3

Therefore, the solution to the equation is x = 8/3.