X(Y-X)+Y(X-Y)=

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Solution for X(Y-X)+Y(X-Y)= equation: 


Simplifying
X(Y + -1X) + Y(X + -1Y) = 0

Reorder the terms:
X(-1X + Y) + Y(X + -1Y) = 0
(-1X * X + Y * X) + Y(X + -1Y) = 0

Reorder the terms:
(XY + -1X2) + Y(X + -1Y) = 0
(XY + -1X2) + Y(X + -1Y) = 0
XY + -1X2 + (X * Y + -1Y * Y) = 0
XY + -1X2 + (XY + -1Y2) = 0

Reorder the terms:
XY + XY + -1X2 + -1Y2 = 0

Combine like terms: XY + XY = 2XY
2XY + -1X2 + -1Y2 = 0

Solving
2XY + -1X2 + -1Y2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-1X + Y)(X + -1Y) = 0


Subproblem 1
Set the factor '(-1X + Y)' equal to zero and attempt to solve:

Simplifying
-1X + Y = 0

Solving
-1X + Y = 0

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

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

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

Divide each side by '-1'.
X = Y

Simplifying
X = Y

Subproblem 2
Set the factor '(X + -1Y)' equal to zero and attempt to solve:

Simplifying
X + -1Y = 0

Solving
X + -1Y = 0

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

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

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

Simplifying
X = Y
Solution
X = {Y, Y}

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