2x^2-2y^2=x^2-2xy+y^2

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Solution for 2x^2-2y^2=x^2-2xy+y^2 equation: 


Simplifying
2x2 + -2y2 = x2 + -2xy + y2

Reorder the terms:
2x2 + -2y2 = -2xy + x2 + y2

Solving
2x2 + -2y2 = -2xy + x2 + y2

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor a trinomial.
(x + -1y)(x + 3y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

Add '-3y' to each side of the equation.
x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y
Solution
x = {y, -3y}

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