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

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


Simplifying
(x2 + -4x * y + -2y2) * dx + (y2 + -4x * y + -2x2) = 0

Multiply x * y
(x2 + -4xy + -2y2) * dx + (y2 + -4x * y + -2x2) = 0

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

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

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

Multiply x * y
-2dxy2 + -4dx2y + dx3 + (y2 + -4xy + -2x2) = 0

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

Remove parenthesis around (-4xy + -2x2 + y2)
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 0

Solving
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 0

Solving for variable 'd'.

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

Add '4xy' to each side of the equation.
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + 4xy + y2 = 0 + 4xy

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

Combine like terms: -4xy + 4xy = 0
-2dxy2 + -4dx2y + dx3 + 0 + -2x2 + y2 = 0 + 4xy
-2dxy2 + -4dx2y + dx3 + -2x2 + y2 = 0 + 4xy
Remove the zero:
-2dxy2 + -4dx2y + dx3 + -2x2 + y2 = 4xy

Add '2x2' to each side of the equation.
-2dxy2 + -4dx2y + dx3 + -2x2 + 2x2 + y2 = 4xy + 2x2

Combine like terms: -2x2 + 2x2 = 0
-2dxy2 + -4dx2y + dx3 + 0 + y2 = 4xy + 2x2
-2dxy2 + -4dx2y + dx3 + y2 = 4xy + 2x2

Add '-1y2' to each side of the equation.
-2dxy2 + -4dx2y + dx3 + y2 + -1y2 = 4xy + 2x2 + -1y2

Combine like terms: y2 + -1y2 = 0
-2dxy2 + -4dx2y + dx3 + 0 = 4xy + 2x2 + -1y2
-2dxy2 + -4dx2y + dx3 = 4xy + 2x2 + -1y2

Reorder the terms:
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 4xy + -4xy + 2x2 + -2x2 + -1y2 + y2

Combine like terms: 4xy + -4xy = 0
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 0 + 2x2 + -2x2 + -1y2 + y2
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 2x2 + -2x2 + -1y2 + y2

Combine like terms: 2x2 + -2x2 = 0
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 0 + -1y2 + y2
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-2dxy2 + -4dx2y + dx3 + -4xy + -2x2 + y2 = 0

The solution to this equation could not be determined.

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