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

3^x(3^(-1) - 1 + 3) = 63

Now, let's simplify the equation further:

3^x(1/3 - 1 + 3) = 63
3^x(4/3) = 63
4(3^x) = 63
4(3^x) = 3^4

Now, we can rewrite 63 as 3^4:

4(3^x) = 3^4

Now, we can equate the exponents on both sides:

4 = x

Therefore, the solution to the equation 3^(x-1) - 3^x + 3^(x+1) = 63 is x = 4.