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

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


Simplifying
6x2 + -1xy + -7y2 = 0

Reorder the terms:
-1xy + 6x2 + -7y2 = 0

Solving
-1xy + 6x2 + -7y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {1.166666667y, -1y}

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