(2x-3)^2-(2x+5)(2x-5)=23 (2x-5)(2x+5)-(2x+3) ^2=-1

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Let's start by expanding the given equations:

Expanding (2x-3)^2:
(2x-3)^2 = (2x-3)(2x-3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9

Expanding (2x+5)(2x-5):
(2x+5)(2x-5) = 4x^2 - 10x + 10x - 25 = 4x^2 - 25

Expanding (2x+3)^2:
(2x+3)^2 = (2x+3)(2x+3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9

Now, substituting these expanded forms into the given equations:

(2x-3)^2 - (2x+5)(2x-5) = 23
4x^2 - 12x + 9 - (4x^2 - 25) = 23
4x^2 - 12x + 9 - 4x^2 + 25 = 23
-12x + 34 = 23
-12x = -11
x = 11/12

(2x-5)(2x+5) - (2x+3)^2 = -1
(4x^2 - 25) - (4x^2 + 12x + 9) = -1
4x^2 - 25 - 4x^2 - 12x - 9 = -1
-12x - 34 = -1
-12x = 33
x = -33/12

Therefore, the solutions to the given equations are x = 11/12 and x = -33/12.