To solve the equation 4^(2x+7) = 64, we can start by expressing both sides of the equation with the same base. Since 4 can be expressed as 2^2, we can rewrite the equation as (2^2)^(2x+7) = 2^6.

Using the exponent rule (a^m)^n = a^(m*n), we can simplify the left side of the equation to 2^(4x+14) = 2^6.

Since the bases are the same, we can equate the exponents: 4x + 14 = 6.

Next, we can solve for x by isolating the variable:

4x = 6 - 14
4x = -8

Dividing both sides by 4, we get:

x = -8/4
x = -2

Therefore, the solution to the equation 4^(2x+7) = 64 is x = -2.