To solve the equation 4x^2 - (3x - 10)^2 = 0, we can expand the square term on the right side and then simplify the equation:

4x^2 - (3x - 10)(3x - 10) = 0
4x^2 - (9x^2 - 60x + 100) = 0
4x^2 - 9x^2 + 60x - 100 = 0
-5x^2 + 60x - 100 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -5, b = 60, and c = -100. Plugging these values into the quadratic formula:

x = (-60 ± √(60^2 - 4(-5)(-100))) / (2(-5))
x = (-60 ± √(3600 - 2000)) / (-10)
x = (-60 ± √(1600)) / (-10)
x = (-60 ± 40) / (-10)

This gives us two possible solutions:

x = (-60 + 40) / (-10) = -20 / (-10) = 2
x = (-60 - 40) / (-10) = -100 / (-10) = 10

Therefore, the solutions to the equation 4x^2 - (3x - 10)^2 = 0 are x = 2 and x = 10.