(4x^2-6y+2xy)dx+(x^2-6x+2)dy=0

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Solution for (4x^2-6y+2xy)dx+(x^2-6x+2)dy=0 equation: 


Simplifying
(4x2 + -6y + 2xy) * dx + (x2 + -6x + 2) * dy = 0

Reorder the terms:
(2xy + 4x2 + -6y) * dx + (x2 + -6x + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + 4x2 + -6y) + (x2 + -6x + 2) * dy = 0
(2xy * dx + 4x2 * dx + -6y * dx) + (x2 + -6x + 2) * dy = 0

Reorder the terms:
(-6dxy + 2dx2y + 4dx3) + (x2 + -6x + 2) * dy = 0
(-6dxy + 2dx2y + 4dx3) + (x2 + -6x + 2) * dy = 0

Reorder the terms:
-6dxy + 2dx2y + 4dx3 + (2 + -6x + x2) * dy = 0

Reorder the terms for easier multiplication:
-6dxy + 2dx2y + 4dx3 + dy(2 + -6x + x2) = 0
-6dxy + 2dx2y + 4dx3 + (2 * dy + -6x * dy + x2 * dy) = 0

Reorder the terms:
-6dxy + 2dx2y + 4dx3 + (-6dxy + dx2y + 2dy) = 0
-6dxy + 2dx2y + 4dx3 + (-6dxy + dx2y + 2dy) = 0

Reorder the terms:
-6dxy + -6dxy + 2dx2y + dx2y + 4dx3 + 2dy = 0

Combine like terms: -6dxy + -6dxy = -12dxy
-12dxy + 2dx2y + dx2y + 4dx3 + 2dy = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-12dxy + 3dx2y + 4dx3 + 2dy = 0

Solving
-12dxy + 3dx2y + 4dx3 + 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(-12xy + 3x2y + 4x3 + 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 '(-12xy + 3x2y + 4x3 + 2y)' equal to zero and attempt to solve:

Simplifying
-12xy + 3x2y + 4x3 + 2y = 0

Solving
-12xy + 3x2y + 4x3 + 2y = 0

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

Add '12xy' to each side of the equation.
-12xy + 3x2y + 4x3 + 12xy + 2y = 0 + 12xy

Reorder the terms:
-12xy + 12xy + 3x2y + 4x3 + 2y = 0 + 12xy

Combine like terms: -12xy + 12xy = 0
0 + 3x2y + 4x3 + 2y = 0 + 12xy
3x2y + 4x3 + 2y = 0 + 12xy
Remove the zero:
3x2y + 4x3 + 2y = 12xy

Add '-3x2y' to each side of the equation.
3x2y + 4x3 + -3x2y + 2y = 12xy + -3x2y

Reorder the terms:
3x2y + -3x2y + 4x3 + 2y = 12xy + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 4x3 + 2y = 12xy + -3x2y
4x3 + 2y = 12xy + -3x2y

Add '-4x3' to each side of the equation.
4x3 + -4x3 + 2y = 12xy + -3x2y + -4x3

Combine like terms: 4x3 + -4x3 = 0
0 + 2y = 12xy + -3x2y + -4x3
2y = 12xy + -3x2y + -4x3

Add '-2y' to each side of the equation.
2y + -2y = 12xy + -3x2y + -4x3 + -2y

Combine like terms: 2y + -2y = 0
0 = 12xy + -3x2y + -4x3 + -2y

Simplifying
0 = 12xy + -3x2y + -4x3 + -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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