(9x-4)^2-(x-12)^2=0

Expand the squares:

81x^2 - 72x + 16 - (x^2 - 24x + 144) = 0

Remove brackets:

81x^2 - 72x + 16 - x^2 + 24x - 144 = 0

Combine like terms:

80x^2 - 48x - 128 = 0

Divide by 16 to simplify:

5x^2 - 3x - 8 = 0

Factor the quadratic equation:

(5x + 4)(x - 2) = 0

Set each factor to zero and solve for x:

5x + 4 = 0
5x = -4
x = -4/5

x - 2 = 0
x = 2

Therefore, the solutions to the equation are x = -4/5 and x = 2.