27x^2+81xy+42y^2=0

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Solution for 27x^2+81xy+42y^2=0 equation: 


Simplifying
27x2 + 81xy + 42y2 = 0

Reorder the terms:
81xy + 27x2 + 42y2 = 0

Solving
81xy + 27x2 + 42y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27xy + 9x2 + 14y2) = 0

Factor a trinomial.
3((3x + 2y)(3x + 7y)) = 0

Ignore the factor 3.

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

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

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

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

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

Subproblem 2
Set the factor '(3x + 7y)' equal to zero and attempt to solve:

Simplifying
3x + 7y = 0

Solving
3x + 7y = 0

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

Add '-7y' to each side of the equation.
3x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
3x + 0 = 0 + -7y
3x = 0 + -7y
Remove the zero:
3x = -7y

Divide each side by '3'.
x = -2.333333333y

Simplifying
x = -2.333333333y
Solution
x = {-0.6666666667y, -2.333333333y}

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