To solve the equation 4^(2x+1) + 4^(2x) = 80, we can rewrite it as:

4^(2x) * 4^1 + 4^(2x) = 80

Simplifying further:

4^(2x) * 4 + 4^(2x) = 80

Now, we can combine the terms with the same base:

4 * 4^(2x) + 4^(2x) = 80

Factoring out 4^(2x):

(4 + 1) * 4^(2x) = 80

5 * 4^(2x) = 80

Dividing both sides by 5:

4^(2x) = 80/5

Simplifying the right side:

4^(2x) = 16

Now, we can rewrite 16 as a power of 4:

4^(2x) = 4^2

Since the bases are the same, the exponents must be equal:

2x = 2

Dividing both sides by 2:

x = 1

Therefore, the solution to the equation 4^(2x+1) + 4^(2x) = 80 is x = 1.