To solve the equation 2^x * 3^(x+1) = 648, we can start by simplifying the equation.

First, we can rewrite 648 as a product of its prime factors: 648 = 2^3 * 3^4.

Now, let's rewrite the equation using the prime factorization of 648:

2^x * 3^(x+1) = 2^3 * 3^4

Next, we can equate the exponents on both sides of the equation:

x + (x + 1) = 3 + 4

2x + 1 = 7

Now, we can solve for x:

2x = 7 - 1

2x = 6

x = 6/2

x = 3

Therefore, the solution to the equation 2^x * 3^(x+1) = 648 is x = 3.