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

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


Simplifying
(6x + 2y2) * dx + (4xy + -2y) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + 2y2) + (4xy + -2y) * dy = 0
(6x * dx + 2y2 * dx) + (4xy + -2y) * dy = 0

Reorder the terms:
(2dxy2 + 6dx2) + (4xy + -2y) * dy = 0
(2dxy2 + 6dx2) + (4xy + -2y) * dy = 0

Reorder the terms for easier multiplication:
2dxy2 + 6dx2 + dy(4xy + -2y) = 0
2dxy2 + 6dx2 + (4xy * dy + -2y * dy) = 0
2dxy2 + 6dx2 + (4dxy2 + -2dy2) = 0

Reorder the terms:
2dxy2 + 4dxy2 + 6dx2 + -2dy2 = 0

Combine like terms: 2dxy2 + 4dxy2 = 6dxy2
6dxy2 + 6dx2 + -2dy2 = 0

Solving
6dxy2 + 6dx2 + -2dy2 = 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), '2d'.
2d(3xy2 + 3x2 + -1y2) = 0

Ignore the factor 2.

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 + 3x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
3xy2 + 3x2 + -1y2 = 0

Solving
3xy2 + 3x2 + -1y2 = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + 3x2 + -3xy2 + -1y2 = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + 3x2 + -1y2 = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + 3x2 + -1y2 = 0 + -3xy2
3x2 + -1y2 = 0 + -3xy2
Remove the zero:
3x2 + -1y2 = -3xy2

Add '-3x2' to each side of the equation.
3x2 + -3x2 + -1y2 = -3xy2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -1y2 = -3xy2 + -3x2
-1y2 = -3xy2 + -3x2

Add 'y2' to each side of the equation.
-1y2 + y2 = -3xy2 + -3x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -3xy2 + -3x2 + y2

Simplifying
0 = -3xy2 + -3x2 + y2

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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