6x^2+xy-7y^2=0

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Solution for 6x^2+xy-7y^2=0 equation: 


Simplifying
6x2 + xy + -7y2 = 0

Reorder the terms:
xy + 6x2 + -7y2 = 0

Solving
xy + 6x2 + -7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -1y)(6x + 7y) = 0


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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

Subproblem 2
Set the factor '(6x + 7y)' equal to zero and attempt to solve:

Simplifying
6x + 7y = 0

Solving
6x + 7y = 0

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

Add '-7y' to each side of the equation.
6x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
6x + 0 = 0 + -7y
6x = 0 + -7y
Remove the zero:
6x = -7y

Divide each side by '6'.
x = -1.166666667y

Simplifying
x = -1.166666667y
Solution
x = {y, -1.166666667y}

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