1) (3x-8)^2-(4x-6)^2+(5x-2)(5x+2)=962) 25(x-2)^2-(x-10)^2=(5x+1)(5x-1)+13) (2x+7)(7-2x)-x(x+2)=49

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1) Expanding the equation gives:

(3x-8)(3x-8) - (4x-6)(4x-6) + (5x-2)(5x+2) = 96
(9x^2 - 24x - 24x + 64) - (16x^2 - 48x + 48x - 36) + (25x^2 - 4) = 96
(9x^2 - 48x + 64) - (16x^2 - 36) + (25x^2 - 4) = 96
9x^2 - 48x + 64 - 16x^2 + 36 + 25x^2 - 4 = 96
18x^2 - 48x + 96 = 96
18x^2 - 48x = 0
18x(x - 2) = 0
x = 0 or x = 2

Therefore, the solutions are x = 0 and x = 2.

2) Expanding the equation gives:

25(x^2 - 4x + 4) - (x^2 - 20x + 100) = 25x^2 - 1 + 13
25x^2 - 100x + 100 - x^2 + 20x - 100 = 25x^2 - 1 + 13
24x^2 - 80x = 12
12(2x^2 - 10x) = 12
2x^2 - 10x = 1
2x^2 - 10x - 1 = 0

Using the quadratic formula to solve for x, we get:

x = (10 ± √(100 + 8)) / 4
x = (10 ± √108) / 4
x = (10 ± 6√3) / 4
x = 5 ± 3√3

Therefore, the solutions are x = 5 + 3√3 and x = 5 - 3√3.

3) Expanding the equation gives:

(14x + 49) - x^2 - 2x = 49
14x + 49 - x^2 - 2x = 49
-x^2 + 12x = 0
x(-x + 12) = 0
x = 0 or x = 12

Therefore, the solutions are x = 0 and x = 12.