X^2-XY-2Y^2=0

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Solution for X^2-XY-2Y^2=0 equation: 


Simplifying
X2 + -1XY + -2Y2 = 0

Reorder the terms:
-1XY + X2 + -2Y2 = 0

Solving
-1XY + X2 + -2Y2 = 0

Solving for variable 'X'.

Factor a trinomial.
(X + -2Y)(X + Y) = 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 + 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 = {2Y, -1Y}

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