(x-y-1)(x-y+1)+(-x+y+1)(x+y-1)+(x-y-1)(x+y+1)=

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Solution for (x-y-1)(x-y+1)+(-x+y+1)(x+y-1)+(x-y-1)(x+y+1)= equation: 


Simplifying
(x + -1y + -1)(x + -1y + 1) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
(-1 + x + -1y)(x + -1y + 1) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
(-1 + x + -1y)(1 + x + -1y) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Multiply (-1 + x + -1y) * (1 + x + -1y)
(-1(1 + x + -1y) + x(1 + x + -1y) + -1y * (1 + x + -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
((1 * -1 + x * -1 + -1y * -1) + x(1 + x + -1y) + -1y * (1 + x + -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
((-1 + -1x + 1y) + x(1 + x + -1y) + -1y * (1 + x + -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
(-1 + -1x + 1y + (1 * x + x * x + -1y * x) + -1y * (1 + x + -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
(-1 + -1x + 1y + (1x + -1xy + x2) + -1y * (1 + x + -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
(-1 + -1x + 1y + (1x + -1xy + x2) + -1y * (1 + x + -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
(-1 + -1x + 1y + 1x + -1xy + x2 + (1 * -1y + x * -1y + -1y * -1y)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
(-1 + -1x + 1y + 1x + -1xy + x2 + (-1xy + -1y + 1y2)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
(-1 + -1x + 1y + 1x + -1xy + x2 + (-1xy + -1y + 1y2)) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
(-1 + -1x + 1x + -1xy + -1xy + x2 + 1y + -1y + 1y2) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Combine like terms: -1x + 1x = 0
(-1 + 0 + -1xy + -1xy + x2 + 1y + -1y + 1y2) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
(-1 + -1xy + -1xy + x2 + 1y + -1y + 1y2) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Combine like terms: -1xy + -1xy = -2xy
(-1 + -2xy + x2 + 1y + -1y + 1y2) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Combine like terms: 1y + -1y = 0
(-1 + -2xy + x2 + 0 + 1y2) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0
(-1 + -2xy + x2 + 1y2) + (-1x + y + 1)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + (1 + -1x + y)(x + y + -1) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + (1 + -1x + y)(-1 + x + y) + (x + -1y + -1)(x + y + 1) = 0

Multiply (1 + -1x + y) * (-1 + x + y)
-1 + -2xy + x2 + 1y2 + (1(-1 + x + y) + -1x * (-1 + x + y) + y(-1 + x + y)) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + ((-1 * 1 + x * 1 + y * 1) + -1x * (-1 + x + y) + y(-1 + x + y)) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + ((-1 + 1x + 1y) + -1x * (-1 + x + y) + y(-1 + x + y)) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1y + (-1 * -1x + x * -1x + y * -1x) + y(-1 + x + y)) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1y + (1x + -1xy + -1x2) + y(-1 + x + y)) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1y + (1x + -1xy + -1x2) + y(-1 + x + y)) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1y + 1x + -1xy + -1x2 + (-1 * y + x * y + y * y)) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1y + 1x + -1xy + -1x2 + (xy + -1y + y2)) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1y + 1x + -1xy + -1x2 + (xy + -1y + y2)) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + (-1 + 1x + 1x + -1xy + xy + -1x2 + 1y + -1y + y2) + (x + -1y + -1)(x + y + 1) = 0

Combine like terms: 1x + 1x = 2x
-1 + -2xy + x2 + 1y2 + (-1 + 2x + -1xy + xy + -1x2 + 1y + -1y + y2) + (x + -1y + -1)(x + y + 1) = 0

Combine like terms: -1xy + xy = 0
-1 + -2xy + x2 + 1y2 + (-1 + 2x + 0 + -1x2 + 1y + -1y + y2) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + (-1 + 2x + -1x2 + 1y + -1y + y2) + (x + -1y + -1)(x + y + 1) = 0

Combine like terms: 1y + -1y = 0
-1 + -2xy + x2 + 1y2 + (-1 + 2x + -1x2 + 0 + y2) + (x + -1y + -1)(x + y + 1) = 0
-1 + -2xy + x2 + 1y2 + (-1 + 2x + -1x2 + y2) + (x + -1y + -1)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + x + -1y)(x + y + 1) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + x + -1y)(1 + x + y) = 0

Multiply (-1 + x + -1y) * (1 + x + y)
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1(1 + x + y) + x(1 + x + y) + -1y * (1 + x + y)) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + ((1 * -1 + x * -1 + y * -1) + x(1 + x + y) + -1y * (1 + x + y)) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + ((-1 + -1x + -1y) + x(1 + x + y) + -1y * (1 + x + y)) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + -1y + (1 * x + x * x + y * x) + -1y * (1 + x + y)) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + -1y + (1x + xy + x2) + -1y * (1 + x + y)) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + -1y + (1x + xy + x2) + -1y * (1 + x + y)) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + -1y + 1x + xy + x2 + (1 * -1y + x * -1y + y * -1y)) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + -1y + 1x + xy + x2 + (-1xy + -1y + -1y2)) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + -1y + 1x + xy + x2 + (-1xy + -1y + -1y2)) = 0

Reorder the terms:
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + -1x + 1x + xy + -1xy + x2 + -1y + -1y + -1y2) = 0

Combine like terms: -1x + 1x = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + 0 + xy + -1xy + x2 + -1y + -1y + -1y2) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + xy + -1xy + x2 + -1y + -1y + -1y2) = 0

Combine like terms: xy + -1xy = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + 0 + x2 + -1y + -1y + -1y2) = 0
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + x2 + -1y + -1y + -1y2) = 0

Combine like terms: -1y + -1y = -2y
-1 + -2xy + x2 + 1y2 + -1 + 2x + -1x2 + y2 + (-1 + x2 + -2y + -1y2) = 0

Reorder the terms:
-1 + -1 + -1 + 2x + -2xy + x2 + -1x2 + x2 + -2y + 1y2 + y2 + -1y2 = 0

Combine like terms: -1 + -1 = -2
-2 + -1 + 2x + -2xy + x2 + -1x2 + x2 + -2y + 1y2 + y2 + -1y2 = 0

Combine like terms: -2 + -1 = -3
-3 + 2x + -2xy + x2 + -1x2 + x2 + -2y + 1y2 + y2 + -1y2 = 0

Combine like terms: x2 + -1x2 = 0
-3 + 2x + -2xy + 0 + x2 + -2y + 1y2 + y2 + -1y2 = 0
-3 + 2x + -2xy + x2 + -2y + 1y2 + y2 + -1y2 = 0

Combine like terms: 1y2 + y2 = 2y2
-3 + 2x + -2xy + x2 + -2y + 2y2 + -1y2 = 0

Combine like terms: 2y2 + -1y2 = 1y2
-3 + 2x + -2xy + x2 + -2y + 1y2 = 0

Solving
-3 + 2x + -2xy + x2 + -2y + 1y2 = 0

Solving for variable 'x'.

The solution to this equation could not be determined.

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