2x(x-y)+y(y-x)=(2x+y)(x-y)

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Solution for 2x(x-y)+y(y-x)=(2x+y)(x-y) equation: 


Simplifying
2x(x + -1y) + y(y + -1x) = (2x + y)(x + -1y)
(x * 2x + -1y * 2x) + y(y + -1x) = (2x + y)(x + -1y)

Reorder the terms:
(-2xy + 2x2) + y(y + -1x) = (2x + y)(x + -1y)
(-2xy + 2x2) + y(y + -1x) = (2x + y)(x + -1y)

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

Reorder the terms:
-2xy + -1xy + 2x2 + y2 = (2x + y)(x + -1y)

Combine like terms: -2xy + -1xy = -3xy
-3xy + 2x2 + y2 = (2x + y)(x + -1y)

Multiply (2x + y) * (x + -1y)
-3xy + 2x2 + y2 = (2x * (x + -1y) + y(x + -1y))
-3xy + 2x2 + y2 = ((x * 2x + -1y * 2x) + y(x + -1y))

Reorder the terms:
-3xy + 2x2 + y2 = ((-2xy + 2x2) + y(x + -1y))
-3xy + 2x2 + y2 = ((-2xy + 2x2) + y(x + -1y))
-3xy + 2x2 + y2 = (-2xy + 2x2 + (x * y + -1y * y))
-3xy + 2x2 + y2 = (-2xy + 2x2 + (xy + -1y2))

Reorder the terms:
-3xy + 2x2 + y2 = (-2xy + xy + 2x2 + -1y2)

Combine like terms: -2xy + xy = -1xy
-3xy + 2x2 + y2 = (-1xy + 2x2 + -1y2)

Add '-2x2' to each side of the equation.
-3xy + 2x2 + -2x2 + y2 = -1xy + 2x2 + -2x2 + -1y2

Combine like terms: 2x2 + -2x2 = 0
-3xy + 0 + y2 = -1xy + 2x2 + -2x2 + -1y2
-3xy + y2 = -1xy + 2x2 + -2x2 + -1y2

Combine like terms: 2x2 + -2x2 = 0
-3xy + y2 = -1xy + 0 + -1y2
-3xy + y2 = -1xy + -1y2

Solving
-3xy + y2 = -1xy + -1y2

Solving for variable 'x'.

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

Add 'xy' to each side of the equation.
-3xy + xy + y2 = -1xy + xy + -1y2

Combine like terms: -3xy + xy = -2xy
-2xy + y2 = -1xy + xy + -1y2

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

Add '-1y2' to each side of the equation.
-2xy + y2 + -1y2 = -1y2 + -1y2

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

Combine like terms: -1y2 + -1y2 = -2y2
-2xy = -2y2

Divide each side by '-2y'.
x = y

Simplifying
x = y

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