Let's simplify the given equation step by step:

9x^2 - 7(x+4)(4-x) - (1 - 4x)^2 = 15

9x^2 - 7((x+4)(4-x)) - (1 - 4x)(1 - 4x) = 15

9x^2 - 7(4x - x^2 + 16 - 4x) - (1 - 4x)(1 - 4x) = 15

9x^2 - 7(16 - x^2) - (1 - 4x)(1 - 4x) = 15

9x^2 - 112 + 7x^2 - (1 - 4x)(1 - 4x) = 15

9x^2 + 7x^2 - 112 - (1 - 4x)^2 = 15

16x^2 - 112 - (1 - 8x + 16x^2) = 15

16x^2 - 112 - 1 + 8x - 16x^2 = 15

8x - 113 = 15

8x = 128

x = 16

Therefore, the solution to the given equation is x = 16.