(y^2-2xy+6x)dx-(x^2-2xy+2)dy=0

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Solution for (y^2-2xy+6x)dx-(x^2-2xy+2)dy=0 equation: 


Simplifying
(y2 + -2xy + 6x) * dx + -1(x2 + -2xy + 2) * dy = 0

Reorder the terms:
(6x + -2xy + y2) * dx + -1(x2 + -2xy + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + -2xy + y2) + -1(x2 + -2xy + 2) * dy = 0
(6x * dx + -2xy * dx + y2 * dx) + -1(x2 + -2xy + 2) * dy = 0

Reorder the terms:
(dxy2 + 6dx2 + -2dx2y) + -1(x2 + -2xy + 2) * dy = 0
(dxy2 + 6dx2 + -2dx2y) + -1(x2 + -2xy + 2) * dy = 0

Reorder the terms:
dxy2 + 6dx2 + -2dx2y + -1(2 + -2xy + x2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 6dx2 + -2dx2y + -1dy(2 + -2xy + x2) = 0
dxy2 + 6dx2 + -2dx2y + (2 * -1dy + -2xy * -1dy + x2 * -1dy) = 0

Reorder the terms:
dxy2 + 6dx2 + -2dx2y + (2dxy2 + -1dx2y + -2dy) = 0
dxy2 + 6dx2 + -2dx2y + (2dxy2 + -1dx2y + -2dy) = 0

Reorder the terms:
dxy2 + 2dxy2 + 6dx2 + -2dx2y + -1dx2y + -2dy = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
3dxy2 + 6dx2 + -2dx2y + -1dx2y + -2dy = 0

Combine like terms: -2dx2y + -1dx2y = -3dx2y
3dxy2 + 6dx2 + -3dx2y + -2dy = 0

Solving
3dxy2 + 6dx2 + -3dx2y + -2dy = 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(3xy2 + 6x2 + -3x2y + -2y) = 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 '(3xy2 + 6x2 + -3x2y + -2y)' equal to zero and attempt to solve:

Simplifying
3xy2 + 6x2 + -3x2y + -2y = 0

Solving
3xy2 + 6x2 + -3x2y + -2y = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + 6x2 + -3x2y + -3xy2 + -2y = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + 6x2 + -3x2y + -2y = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + 6x2 + -3x2y + -2y = 0 + -3xy2
6x2 + -3x2y + -2y = 0 + -3xy2
Remove the zero:
6x2 + -3x2y + -2y = -3xy2

Add '-6x2' to each side of the equation.
6x2 + -3x2y + -6x2 + -2y = -3xy2 + -6x2

Reorder the terms:
6x2 + -6x2 + -3x2y + -2y = -3xy2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + -3x2y + -2y = -3xy2 + -6x2
-3x2y + -2y = -3xy2 + -6x2

Add '3x2y' to each side of the equation.
-3x2y + 3x2y + -2y = -3xy2 + -6x2 + 3x2y

Combine like terms: -3x2y + 3x2y = 0
0 + -2y = -3xy2 + -6x2 + 3x2y
-2y = -3xy2 + -6x2 + 3x2y

Add '2y' to each side of the equation.
-2y + 2y = -3xy2 + -6x2 + 3x2y + 2y

Combine like terms: -2y + 2y = 0
0 = -3xy2 + -6x2 + 3x2y + 2y

Simplifying
0 = -3xy2 + -6x2 + 3x2y + 2y

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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