(x^2-4xy-2y^2)dx+(y^2-4xy-2x^2)dy=0

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Solution for (x^2-4xy-2y^2)dx+(y^2-4xy-2x^2)dy=0 equation: 


Simplifying
(x2 + -4xy + -2y2) * dx + (y2 + -4xy + -2x2) * dy = 0

Reorder the terms:
(-4xy + x2 + -2y2) * dx + (y2 + -4xy + -2x2) * dy = 0

Reorder the terms for easier multiplication:
dx(-4xy + x2 + -2y2) + (y2 + -4xy + -2x2) * dy = 0
(-4xy * dx + x2 * dx + -2y2 * dx) + (y2 + -4xy + -2x2) * dy = 0

Reorder the terms:
(-2dxy2 + -4dx2y + dx3) + (y2 + -4xy + -2x2) * dy = 0
(-2dxy2 + -4dx2y + dx3) + (y2 + -4xy + -2x2) * dy = 0

Reorder the terms:
-2dxy2 + -4dx2y + dx3 + (-4xy + -2x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
-2dxy2 + -4dx2y + dx3 + dy(-4xy + -2x2 + y2) = 0
-2dxy2 + -4dx2y + dx3 + (-4xy * dy + -2x2 * dy + y2 * dy) = 0
-2dxy2 + -4dx2y + dx3 + (-4dxy2 + -2dx2y + dy3) = 0

Reorder the terms:
-2dxy2 + -4dxy2 + -4dx2y + -2dx2y + dx3 + dy3 = 0

Combine like terms: -2dxy2 + -4dxy2 = -6dxy2
-6dxy2 + -4dx2y + -2dx2y + dx3 + dy3 = 0

Combine like terms: -4dx2y + -2dx2y = -6dx2y
-6dxy2 + -6dx2y + dx3 + dy3 = 0

Solving
-6dxy2 + -6dx2y + dx3 + dy3 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(-6xy2 + -6x2y + x3 + y3) = 0


Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(-6xy2 + -6x2y + x3 + y3)' equal to zero and attempt to solve:

Simplifying
-6xy2 + -6x2y + x3 + y3 = 0

Solving
-6xy2 + -6x2y + x3 + y3 = 0

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

Add '6xy2' to each side of the equation.
-6xy2 + -6x2y + x3 + 6xy2 + y3 = 0 + 6xy2

Reorder the terms:
-6xy2 + 6xy2 + -6x2y + x3 + y3 = 0 + 6xy2

Combine like terms: -6xy2 + 6xy2 = 0
0 + -6x2y + x3 + y3 = 0 + 6xy2
-6x2y + x3 + y3 = 0 + 6xy2
Remove the zero:
-6x2y + x3 + y3 = 6xy2

Add '6x2y' to each side of the equation.
-6x2y + x3 + 6x2y + y3 = 6xy2 + 6x2y

Reorder the terms:
-6x2y + 6x2y + x3 + y3 = 6xy2 + 6x2y

Combine like terms: -6x2y + 6x2y = 0
0 + x3 + y3 = 6xy2 + 6x2y
x3 + y3 = 6xy2 + 6x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + y3 = 6xy2 + 6x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y3 = 6xy2 + 6x2y + -1x3
y3 = 6xy2 + 6x2y + -1x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = 6xy2 + 6x2y + -1x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = 6xy2 + 6x2y + -1x3 + -1y3

Simplifying
0 = 6xy2 + 6x2y + -1x3 + -1y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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