To solve the given equation:

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

We can simplify the equation by factoring out common terms:

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

Now, evaluate the expression within the parentheses:

3^(2x-2) (9 - 6 - 2) = 1
3^(2x-2) (1) = 1
3^(2x-2) = 1

Now, we know that 3^0 = 1. Therefore, we can conclude that:

2x - 2 = 0
2x = 2
x = 1

So, x = 1 is the solution to the given equation.