6x^2+11xy-7y^2=0

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Solution for 6x^2+11xy-7y^2=0 equation: 


Simplifying
6x2 + 11xy + -7y2 = 0

Reorder the terms:
11xy + 6x2 + -7y2 = 0

Solving
11xy + 6x2 + -7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -1y)(3x + 7y) = 0


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

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

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 = {0.5y, -2.333333333y}

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