(X+Y)x=Yx+Zx

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Solution for (X+Y)x=Yx+Zx equation: 


Simplifying
(X + Y) * x = Yx + Zx

Reorder the terms for easier multiplication:
x(X + Y) = Yx + Zx
(X * x + Y * x) = Yx + Zx
(xX + xY) = Yx + Zx

Add '-1xY' to each side of the equation.
xX + xY + -1xY = xY + -1xY + xZ

Combine like terms: xY + -1xY = 0
xX + 0 = xY + -1xY + xZ
xX = xY + -1xY + xZ

Combine like terms: xY + -1xY = 0
xX = 0 + xZ
xX = xZ

Solving
xX = xZ

Solving for variable 'x'.

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

Add '-1xZ' to each side of the equation.
xX + -1xZ = xZ + -1xZ

Combine like terms: xZ + -1xZ = 0
xX + -1xZ = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(X + -1Z) = 0


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 '(X + -1Z)' equal to zero and attempt to solve:

Simplifying
X + -1Z = 0

Solving
X + -1Z = 0

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

Add '-1X' to each side of the equation.
X + -1X + -1Z = 0 + -1X

Combine like terms: X + -1X = 0
0 + -1Z = 0 + -1X
-1Z = 0 + -1X
Remove the zero:
-1Z = -1X

Add 'Z' to each side of the equation.
-1Z + Z = -1X + Z

Combine like terms: -1Z + Z = 0
0 = -1X + Z

Simplifying
0 = -1X + Z

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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