6x^2+23xy+21y^2=0

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Solution for 6x^2+23xy+21y^2=0 equation: 


Simplifying
6x2 + 23xy + 21y2 = 0

Reorder the terms:
23xy + 6x2 + 21y2 = 0

Solving
23xy + 6x2 + 21y2 = 0

Solving for variable 'x'.

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


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 '(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 = {-1.5y, -2.333333333y}

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