To solve this equation, we will first simplify the left side of the equation:

3(x-7) + 4^2 = 5^2

3(x-7) + 16 = 25

Next, distribute the 3 to the terms inside the parentheses:

3x - 21 + 16 = 25

Combine like terms:

3x - 5 = 25

Now, isolate the variable by adding 5 to both sides:

3x = 30

Finally, divide both sides by 3 to solve for x:

x = 10