2y^2+xy-3x^2=0

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Solution for 2y^2+xy-3x^2=0 equation: 


Simplifying
2y2 + xy + -3x2 = 0

Reorder the terms:
xy + -3x2 + 2y2 = 0

Solving
xy + -3x2 + 2y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-3x + -2y)' equal to zero and attempt to solve:

Simplifying
-3x + -2y = 0

Solving
-3x + -2y = 0

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

Add '2y' to each side of the equation.
-3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-3x + 0 = 0 + 2y
-3x = 0 + 2y
Remove the zero:
-3x = 2y

Divide each side by '-3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

Subproblem 2
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
Solution
x = {-0.6666666667y, y}

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