To solve this equation, we need to first simplify the left side by distributing the terms in the parentheses:

4x(x-1) - (2x+5)(2x-5) = 1

4x^2 - 4x - (4x^2 - 10x + 5) = 1
4x^2 - 4x - 4x^2 + 10x - 5 = 1
4x^2 - 4x - 4x^2 + 10x - 5 = 1
6x - 5 = 1

Now, add 5 to both sides to isolate x:

6x = 6

Finally, divide both sides by 6 to solve for x:

x = 1

Therefore, the solution to the equation 4x(x-1) - (2x+5)(2x-5) = 1 is x = 1.