To solve the equation 7*4^(x-1) + 4^(x+1) = 23, we can simplify it by noticing that both terms have a common factor of 4^(x-1). We can factor it out to get:

4^(x-1) * (7 + 4^2) = 23

Simplifying further:

4^(x-1) * (7 + 16) = 23

4^(x-1) * 23 = 23

Now, divide both sides of the equation by 23:

4^(x-1) = 1

Since any number raised to the power of 0 is equal to 1, we can conclude that:

x - 1 = 0

Adding 1 to both sides of the equation:

x = 1

Therefore, the solution to the equation is x = 1.