To solve this equation, you can first rewrite it as a quadratic equation in terms of (3^(2x)).

Let (y = 3^(2x)), the equation becomes:
((y - 1)(y^2 + y + 1) = 26)

Expanding the left side, we get:
(y^3 + y^2 + y - y^2 - y - 1 = 26)

Simplify:
(y^3 - 1 = 26)

Now, we can rewrite this equation back in terms of (3^(2x)):
(3^(2x)^3 - 1 = 26)

((3^(2x))^3 = 27)

(3^(6x) = 27)

(3^(6x) = 3^3)

Since the bases are the same, we can equate the exponents:
(6x = 3)

(x = 1/2)

Therefore, the solution to the equation is (x = 1/2).