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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
2xy + 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(y + 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 '(y + z)' equal to zero and attempt to solve:

Simplifying
y + z = 0

Solving
y + z = 0

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

Add '-1y' to each side of the equation.
y + -1y + z = 0 + -1y

Combine like terms: y + -1y = 0
0 + z = 0 + -1y
z = 0 + -1y
Remove the zero:
z = -1y

Add '-1z' to each side of the equation.
z + -1z = -1y + -1z

Combine like terms: z + -1z = 0
0 = -1y + -1z

Simplifying
0 = -1y + -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}