5x^2+4xy+y^2=2y^2

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Solution for 5x^2+4xy+y^2=2y^2 equation: 


Simplifying
5x2 + 4xy + y2 = 2y2

Reorder the terms:
4xy + 5x2 + y2 = 2y2

Solving
4xy + 5x2 + y2 = 2y2

Solving for variable 'x'.

Combine like terms: y2 + -2y2 = -1y2
4xy + 5x2 + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
4xy + 5x2 + -1y2 = 0

Factor a trinomial.
(5x + -1y)(x + y) = 0


Subproblem 1
Set the factor '(5x + -1y)' equal to zero and attempt to solve:

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y

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 = {0.2y, -1y}

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