To solve for x, we first need to expand and simplify both sides of the equation:

Left side:
4(x-1)² = 4(x² - 2x + 1) = 4x² - 8x + 4

-3(x-5)(x+5) = -3(x² - 25) = -3x² + 75

Therefore, the left side of the equation becomes:
4x² - 8x + 4 - 3x² + 75 + x = x(x+7)

Simplify the left side:
x² - 7x + 79 = x² + 7x

Now we have:
-x + 79 = 7x

Rearrange the equation:
8x = 79

Divide by 8:
x = 79/8

Therefore, the solution to the equation is:
x = 9.875