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

Solution for (x+y-z)(x+y+z)=0 equation:

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

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

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

Reorder the terms:
(xy + xz + x2 + (xy + yz + y2) + -1z * (x + y + z)) = 0
(xy + xz + x2 + (xy + yz + y2) + -1z * (x + y + z)) = 0
(xy + xz + x2 + xy + yz + y2 + (x * -1z + y * -1z + z * -1z)) = 0
(xy + xz + x2 + xy + yz + y2 + (-1xz + -1yz + -1z2)) = 0

Reorder the terms:
(xy + xy + xz + -1xz + x2 + yz + -1yz + y2 + -1z2) = 0

Combine like terms: xy + xy = 2xy
(2xy + xz + -1xz + x2 + yz + -1yz + y2 + -1z2) = 0

Combine like terms: xz + -1xz = 0
(2xy + 0 + x2 + yz + -1yz + y2 + -1z2) = 0
(2xy + x2 + yz + -1yz + y2 + -1z2) = 0

Combine like terms: yz + -1yz = 0
(2xy + x2 + 0 + y2 + -1z2) = 0
(2xy + x2 + y2 + -1z2) = 0

Solving
2xy + x2 + y2 + -1z2 = 0

Solving for variable 'x'.

The solution to this equation could not be determined.