2y^2+18xy+36x^2=0

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Solution for 2y^2+18xy+36x^2=0 equation: 


Simplifying
2y2 + 18xy + 36x2 = 0

Reorder the terms:
18xy + 36x2 + 2y2 = 0

Solving
18xy + 36x2 + 2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9xy + 18x2 + y2) = 0

Factor a trinomial.
2((6x + y)(3x + y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6x + y)' equal to zero and attempt to solve:

Simplifying
6x + y = 0

Solving
6x + y = 0

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

Add '-1y' to each side of the equation.
6x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
6x + 0 = 0 + -1y
6x = 0 + -1y
Remove the zero:
6x = -1y

Divide each side by '6'.
x = -0.1666666667y

Simplifying
x = -0.1666666667y

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

Simplifying
3x + y = 0

Solving
3x + y = 0

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

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

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

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

Simplifying
x = -0.3333333333y
Solution
x = {-0.1666666667y, -0.3333333333y}

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