=5x^2+7xy-6y^2

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Solution for =5x^2+7xy-6y^2 equation: 


Simplifying
0 = 5x2 + 7xy + -6y2

Reorder the terms:
0 = 7xy + 5x2 + -6y2

Solving
0 = 7xy + 5x2 + -6y2

Solving for variable 'x'.
Remove the zero:
-7xy + -5x2 + 6y2 = 7xy + 5x2 + -6y2 + -7xy + -5x2 + 6y2

Reorder the terms:
-7xy + -5x2 + 6y2 = 7xy + -7xy + 5x2 + -5x2 + -6y2 + 6y2

Combine like terms: 7xy + -7xy = 0
-7xy + -5x2 + 6y2 = 0 + 5x2 + -5x2 + -6y2 + 6y2
-7xy + -5x2 + 6y2 = 5x2 + -5x2 + -6y2 + 6y2

Combine like terms: 5x2 + -5x2 = 0
-7xy + -5x2 + 6y2 = 0 + -6y2 + 6y2
-7xy + -5x2 + 6y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
-7xy + -5x2 + 6y2 = 0

Factor a trinomial.
(-1x + -2y)(5x + -3y) = 0


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

Simplifying
-1x + -2y = 0

Solving
-1x + -2y = 0

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

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

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

Divide each side by '-1'.
x = -2y

Simplifying
x = -2y

Subproblem 2
Set the factor '(5x + -3y)' equal to zero and attempt to solve:

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

Add '3y' to each side of the equation.
5x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
5x + 0 = 0 + 3y
5x = 0 + 3y
Remove the zero:
5x = 3y

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {-2y, 0.6y}

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