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

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


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

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

Reorder the terms for easier multiplication:
dx(6x + -2xy + x2) + (x2 + -2xy + 2) * dy = 0
(6x * dx + -2xy * dx + x2 * dx) + (x2 + -2xy + 2) * dy = 0
(6dx2 + -2dx2y + dx3) + (x2 + -2xy + 2) * dy = 0

Reorder the terms:
6dx2 + -2dx2y + dx3 + (2 + -2xy + x2) * dy = 0

Reorder the terms for easier multiplication:
6dx2 + -2dx2y + dx3 + dy(2 + -2xy + x2) = 0
6dx2 + -2dx2y + dx3 + (2 * dy + -2xy * dy + x2 * dy) = 0

Reorder the terms:
6dx2 + -2dx2y + dx3 + (-2dxy2 + dx2y + 2dy) = 0
6dx2 + -2dx2y + dx3 + (-2dxy2 + dx2y + 2dy) = 0

Reorder the terms:
-2dxy2 + 6dx2 + -2dx2y + dx2y + dx3 + 2dy = 0

Combine like terms: -2dx2y + dx2y = -1dx2y
-2dxy2 + 6dx2 + -1dx2y + dx3 + 2dy = 0

Solving
-2dxy2 + 6dx2 + -1dx2y + dx3 + 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(-2xy2 + 6x2 + -1x2y + x3 + 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 '(-2xy2 + 6x2 + -1x2y + x3 + 2y)' equal to zero and attempt to solve:

Simplifying
-2xy2 + 6x2 + -1x2y + x3 + 2y = 0

Solving
-2xy2 + 6x2 + -1x2y + x3 + 2y = 0

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

Add '2xy2' to each side of the equation.
-2xy2 + 6x2 + -1x2y + x3 + 2xy2 + 2y = 0 + 2xy2

Reorder the terms:
-2xy2 + 2xy2 + 6x2 + -1x2y + x3 + 2y = 0 + 2xy2

Combine like terms: -2xy2 + 2xy2 = 0
0 + 6x2 + -1x2y + x3 + 2y = 0 + 2xy2
6x2 + -1x2y + x3 + 2y = 0 + 2xy2
Remove the zero:
6x2 + -1x2y + x3 + 2y = 2xy2

Add '-6x2' to each side of the equation.
6x2 + -1x2y + x3 + -6x2 + 2y = 2xy2 + -6x2

Reorder the terms:
6x2 + -6x2 + -1x2y + x3 + 2y = 2xy2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + -1x2y + x3 + 2y = 2xy2 + -6x2
-1x2y + x3 + 2y = 2xy2 + -6x2

Add 'x2y' to each side of the equation.
-1x2y + x3 + x2y + 2y = 2xy2 + -6x2 + x2y

Reorder the terms:
-1x2y + x2y + x3 + 2y = 2xy2 + -6x2 + x2y

Combine like terms: -1x2y + x2y = 0
0 + x3 + 2y = 2xy2 + -6x2 + x2y
x3 + 2y = 2xy2 + -6x2 + x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + 2y = 2xy2 + -6x2 + x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 2y = 2xy2 + -6x2 + x2y + -1x3
2y = 2xy2 + -6x2 + x2y + -1x3

Add '-2y' to each side of the equation.
2y + -2y = 2xy2 + -6x2 + x2y + -1x3 + -2y

Combine like terms: 2y + -2y = 0
0 = 2xy2 + -6x2 + x2y + -1x3 + -2y

Simplifying
0 = 2xy2 + -6x2 + x2y + -1x3 + -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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