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

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


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

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

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

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

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

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

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

Reorder the terms:
2xy + xz + x2 + yz + y2 + -1(-1xy + -1xy + -1xz + x2 + 1yz + 1y2) = 0

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

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

Combine like terms: 2xy + 2xy = 4xy
4xy + xz + 1xz + x2 + -1x2 + yz + -1yz + y2 + -1y2 = 0

Combine like terms: xz + 1xz = 2xz
4xy + 2xz + x2 + -1x2 + yz + -1yz + y2 + -1y2 = 0

Combine like terms: x2 + -1x2 = 0
4xy + 2xz + 0 + yz + -1yz + y2 + -1y2 = 0
4xy + 2xz + yz + -1yz + y2 + -1y2 = 0

Combine like terms: yz + -1yz = 0
4xy + 2xz + 0 + y2 + -1y2 = 0
4xy + 2xz + y2 + -1y2 = 0

Combine like terms: y2 + -1y2 = 0
4xy + 2xz + 0 = 0
4xy + 2xz = 0

Solving
4xy + 2xz = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2y + z) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(2y + z)' equal to zero and attempt to solve: Simplifying 2y + z = 0 Solving 2y + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 2y + -2y + z = 0 + -2y Combine like terms: 2y + -2y = 0 0 + z = 0 + -2y z = 0 + -2y Remove the zero: z = -2y Add '-1z' to each side of the equation. z + -1z = -2y + -1z Combine like terms: z + -1z = 0 0 = -2y + -1z Simplifying 0 = -2y + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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