1) (x-2)^2 - (x+3)(x-3) = 2
Expanding the left side:
(x^2 - 4x + 4) - (x^2 - 3x - 3x + 9) = 2
x^2 - 4x + 4 - x^2 + 6x - 9 = 2
2x - 5 = 2
2x = 7
x = 7/2

2) (7y+1)^2 - (y+7)^2 = 48(y-1)(y+1)
Expanding the left side:
(49y^2 + 14y + 1) - (y^2 + 14y + 49) = 48(y^2 - 1)
48y^2 + 48 - 49 = 48y^2 - 48
-1 = 48
This equation is not possible, so there is no solution for this case.

3) (x+2)(x^2+2x+4) - x(x+3)(x-3) = 26
Expanding and simplifying the left side:
(x^3 + 2x^2 + 4x + 2x^2 + 4x + 8) - (x^3 - 3x^2 + 3x^2 -9x) = 26
x^3 + 2x^2 + 4x + 2x^2 + 4x + 8 - x^3 + 3x^2 - 3x^2 + 9x = 26
8x + 8 = 26
8x = 18
x = 18/8
x = 9/4

Therefore, the solutions are:
1) x = 7/2
3) x = 9/4