Let's expand and simplify the expression:

(1.6x + 1)(1.6x - 1) - 64x(1 - 0.04x) = 0

Expanding the first set of parentheses:
= (1.6x)(1.6x) + (1.6x)(-1) + (1)(1.6x) + (1)(-1) - 64x(1 - 0.04x)

= 2.56x^2 - 1.6x + 1.6x - 1 - 64x + 2.56x

= 2.56x^2 - 62.4x - 1

Setting the expression equal to zero:
2.56x^2 - 62.4x - 1 = 0

Now we can use the quadratic formula to find the values of x that satisfy this equation:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2.56, b = -62.4, and c = -1.

Plugging in the values:
x = (62.4 ± √((-62.4)^2 - 4(2.56)(-1))) / 2(2.56)
x = (62.4 ± √(3893.76 + 10.24)) / 5.12
x = (62.4 ± √3904) / 5.12
x = (62.4 ± 62.56) / 5.12

Thus, the solutions for x are:
x = (62.4 + 62.56) / 5.12 = 124.96 / 5.12 = 24.453125
x = (62.4 - 62.56) / 5.12 = -0.16 / 5.12 = -0.03125

Therefore, the solutions for x are x ≈ 24.453125 and x ≈ -0.03125.