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

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


Simplifying
x2 + xy + -6y2 = 0

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

Solving
xy + x2 + -6y2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2y

Subproblem 2

Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3y

Solution

x = {2y, -3y}

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