Expanding the terms on the left side of the equation, we get:

(x-8)(x+5) = x^2 + 5x - 8x - 40 = x^2 - 3x - 40

(x-6)(x+6) = x^2 + 6x - 6x - 36 = x^2 - 36

Substitute these back into the original equation:

(x^2 - 3x - 40) - (x^2 - 36) = 8

Expanding and simplifying further:

x^2 - 3x - 40 - x^2 + 36 = 8

-3x - 4 = 8

-3x = 12

x = -4

Therefore, the value of x that satisfies the equation is -4.