3x^2+y^2=4xy

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Solution for 3x^2+y^2=4xy equation: 


Simplifying
3x2 + y2 = 4xy

Solving
3x2 + y2 = 4xy

Solving for variable 'x'.

Reorder the terms:
-4xy + 3x2 + y2 = 4xy + -4xy

Combine like terms: 4xy + -4xy = 0
-4xy + 3x2 + y2 = 0

Factor a trinomial.
(x + -1y)(3x + -1y) = 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 '(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
Solution
x = {y, 0.3333333333y}

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