To solve this equation, we will first rewrite it as follows:

3^x - 3^(2-x) - 8 = 0

Next, we can use the property of exponents that states 3^(a+b) = 3^a * 3^b, and 3^(a-b) = 3^a / 3^b.

Therefore, we can rewrite the equation as:

3^x - (3^2 3^(-x)) - 8 = 0
3^x - 9 (1/3^x) - 8 = 0
3^x - 9/3^x - 8 = 0

Now, let's substitute u = 3^x:

u - 9/u - 8 = 0

Multiply through by u to clear the fraction:

u^2 - 9 - 8u = 0

Rearranging the equation:

u^2 - 8u - 9 = 0

Now, we can factor the quadratic equation:

(u - 9)(u + 1) = 0

Setting each factor to zero:

u - 9 = 0 or u + 1 = 0

u = 9 or u = -1

Since u = 3^x, we have two possible solutions for x:

1) 3^x = 9
x = 2

2) 3^x = -1
This solution is not valid as we cannot raise a positive number to any power and get a negative result.

Therefore, the only solution to the equation is x = 2.