x^2+9xy+18y^2=0

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Solution for x^2+9xy+18y^2=0 equation: 


Simplifying
x2 + 9xy + 18y2 = 0

Reorder the terms:
9xy + x2 + 18y2 = 0

Solving
9xy + x2 + 18y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(x + 6y)' equal to zero and attempt to solve:

Simplifying
x + 6y = 0

Solving
x + 6y = 0

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

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

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

Simplifying
x = -6y
Solution
x = {-3y, -6y}

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