To solve this equation, we can first simplify the left side by factoring out a common factor of 3^(x-2):

3^(x+1) - 43^(x-2) = 69
33^x - 43^x = 69
(3-4)3^x = 69
-3*3^x = 69
-3^x = 69/3
-3^x = 23

Now, we can rewrite -3^x as 1/(-3^x) and rewrite 23 as 3^2:

1/3^x = 3^2

To solve for x, we can rewrite both sides with the same base:

3^(-x) = 3^2

Since the bases are the same, we can set the exponents equal to each other:

-x = 2

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