4x^2=y^2-2xy+x^2

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Solution for 4x^2=y^2-2xy+x^2 equation: 


Simplifying
4x2 = y2 + -2xy + x2

Reorder the terms:
4x2 = -2xy + x2 + y2

Solving
4x2 = -2xy + x2 + y2

Solving for variable 'x'.

Reorder the terms:
2xy + 4x2 + -1x2 + -1y2 = -2xy + x2 + y2 + 2xy + -1x2 + -1y2

Combine like terms: 4x2 + -1x2 = 3x2
2xy + 3x2 + -1y2 = -2xy + x2 + y2 + 2xy + -1x2 + -1y2

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

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

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

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

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


Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {0.3333333333y, -1y}

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