6x^2+33xy+36y^2=0

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Solution for 6x^2+33xy+36y^2=0 equation: 


Simplifying
6x2 + 33xy + 36y2 = 0

Reorder the terms:
33xy + 6x2 + 36y2 = 0

Solving
33xy + 6x2 + 36y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(11xy + 2x2 + 12y2) = 0

Factor a trinomial.
3((2x + 3y)(x + 4y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2x + 3y)' equal to zero and attempt to solve:

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

Subproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

Add '-4y' to each side of the equation.
x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
x + 0 = 0 + -4y
x = 0 + -4y
Remove the zero:
x = -4y

Simplifying
x = -4y
Solution
x = {-1.5y, -4y}

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