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

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


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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2yz' to each side of the equation.
x2 + -2yz + -1y2 + 2yz + -1z2 = 0 + 2yz

Reorder the terms:
x2 + -2yz + 2yz + -1y2 + -1z2 = 0 + 2yz

Combine like terms: -2yz + 2yz = 0
x2 + 0 + -1y2 + -1z2 = 0 + 2yz
x2 + -1y2 + -1z2 = 0 + 2yz
Remove the zero:
x2 + -1y2 + -1z2 = 2yz

Add 'y2' to each side of the equation.
x2 + -1y2 + y2 + -1z2 = 2yz + y2

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

Add 'z2' to each side of the equation.
x2 + -1z2 + z2 = 2yz + y2 + z2

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

Simplifying
x2 = 2yz + y2 + z2

Reorder the terms:
x2 + -2yz + -1y2 + -1z2 = 2yz + -2yz + y2 + -1y2 + z2 + -1z2

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

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

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

The solution to this equation could not be determined.

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