18x^2-31xy+6y^2=0

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Solution for 18x^2-31xy+6y^2=0 equation: 


Simplifying
18x2 + -31xy + 6y2 = 0

Reorder the terms:
-31xy + 18x2 + 6y2 = 0

Solving
-31xy + 18x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -3y)(9x + -2y) = 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 '(9x + -2y)' equal to zero and attempt to solve:

Simplifying
9x + -2y = 0

Solving
9x + -2y = 0

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

Add '2y' to each side of the equation.
9x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
9x + 0 = 0 + 2y
9x = 0 + 2y
Remove the zero:
9x = 2y

Divide each side by '9'.
x = 0.2222222222y

Simplifying
x = 0.2222222222y
Solution
x = {1.5y, 0.2222222222y}

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