5x^2-31xy+6y^2=0

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Solution for 5x^2-31xy+6y^2=0 equation: 


Simplifying
5x2 + -31xy + 6y2 = 0

Reorder the terms:
-31xy + 5x2 + 6y2 = 0

Solving
-31xy + 5x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -6y)(5x + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5x + -1y)' equal to zero and attempt to solve:

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y
Solution
x = {6y, 0.2y}

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