(x+y)(x-y)+(x+y)(y+z)-(x+y)(y-z)=

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


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

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

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

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

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

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

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

Multiply (x + y) * (y + -1z)
x2 + -1y2 + xy + xz + yz + y2 + -1(x(y + -1z) + y(y + -1z)) = 0
x2 + -1y2 + xy + xz + yz + y2 + -1((y * x + -1z * x) + y(y + -1z)) = 0
x2 + -1y2 + xy + xz + yz + y2 + -1((xy + -1xz) + y(y + -1z)) = 0
x2 + -1y2 + xy + xz + yz + y2 + -1(xy + -1xz + (y * y + -1z * y)) = 0

Reorder the terms:
x2 + -1y2 + xy + xz + yz + y2 + -1(xy + -1xz + (-1yz + y2)) = 0
x2 + -1y2 + xy + xz + yz + y2 + -1(xy + -1xz + (-1yz + y2)) = 0
x2 + -1y2 + xy + xz + yz + y2 + -1(xy + -1xz + -1yz + y2) = 0
x2 + -1y2 + xy + xz + yz + y2 + (xy * -1 + -1xz * -1 + -1yz * -1 + y2 * -1) = 0
x2 + -1y2 + xy + xz + yz + y2 + (-1xy + 1xz + 1yz + -1y2) = 0

Reorder the terms:
xy + -1xy + xz + 1xz + x2 + yz + 1yz + -1y2 + y2 + -1y2 = 0

Combine like terms: xy + -1xy = 0
0 + xz + 1xz + x2 + yz + 1yz + -1y2 + y2 + -1y2 = 0
xz + 1xz + x2 + yz + 1yz + -1y2 + y2 + -1y2 = 0

Combine like terms: xz + 1xz = 2xz
2xz + x2 + yz + 1yz + -1y2 + y2 + -1y2 = 0

Combine like terms: yz + 1yz = 2yz
2xz + x2 + 2yz + -1y2 + y2 + -1y2 = 0

Combine like terms: -1y2 + y2 = 0
2xz + x2 + 2yz + 0 + -1y2 = 0
2xz + x2 + 2yz + -1y2 = 0

Solving
2xz + x2 + 2yz + -1y2 = 0

Solving for variable 'x'.

The solution to this equation could not be determined.

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