1) Expanding the equation, we get:

(x + 4)^2 - (x - 2)(x + 2) = x^2 + 8x + 16 - (x^2 - 2x + 2x - 4)
= x^2 + 8x + 16 - (x^2 - 4)
= x^2 + 8x + 16 - x^2 + 4
= 8x + 20 = 0
8x = -20
x = -20/8
x = -5/2

Therefore, the solution to the equation (х+4)^2 - ( x - 2 )( x + 2 ) =0 is x = -5/2.

2) Expanding the equation, we get:

(2x - 5)^2 - (2x - 3)(2x + 3) = (2x)^2 - 252x + 5^2 - (4x^2 - 32x + 32x - 3^2)
= 4x^2 - 20x + 25 - 4x^2 + 12x + 12x - 9
= -20x + 25 - 9
= -20x + 16 = 0
20x = 16
x = 16/20
x = 4/5

Therefore, the solution to the equation (2x -5)^2 - (2x - 3 )( 2x + 3) =0 is x = 4/5.