(3x^2+2y^2)dx+(4xy+6y^2)dy=0

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Solution for (3x^2+2y^2)dx+(4xy+6y^2)dy=0 equation: 


Simplifying
(3x2 + 2y2) * dx + (4xy + 6y2) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + 2y2) + (4xy + 6y2) * dy = 0
(3x2 * dx + 2y2 * dx) + (4xy + 6y2) * dy = 0

Reorder the terms:
(2dxy2 + 3dx3) + (4xy + 6y2) * dy = 0
(2dxy2 + 3dx3) + (4xy + 6y2) * dy = 0

Reorder the terms for easier multiplication:
2dxy2 + 3dx3 + dy(4xy + 6y2) = 0
2dxy2 + 3dx3 + (4xy * dy + 6y2 * dy) = 0
2dxy2 + 3dx3 + (4dxy2 + 6dy3) = 0

Reorder the terms:
2dxy2 + 4dxy2 + 3dx3 + 6dy3 = 0

Combine like terms: 2dxy2 + 4dxy2 = 6dxy2
6dxy2 + 3dx3 + 6dy3 = 0

Solving
6dxy2 + 3dx3 + 6dy3 = 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), '3d'.
3d(2xy2 + x3 + 2y3) = 0

Ignore the factor 3.

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 + x3 + 2y3)' equal to zero and attempt to solve:

Simplifying
2xy2 + x3 + 2y3 = 0

Solving
2xy2 + x3 + 2y3 = 0

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

Add '-2xy2' to each side of the equation.
2xy2 + x3 + -2xy2 + 2y3 = 0 + -2xy2

Reorder the terms:
2xy2 + -2xy2 + x3 + 2y3 = 0 + -2xy2

Combine like terms: 2xy2 + -2xy2 = 0
0 + x3 + 2y3 = 0 + -2xy2
x3 + 2y3 = 0 + -2xy2
Remove the zero:
x3 + 2y3 = -2xy2

Add '-1x3' to each side of the equation.
x3 + -1x3 + 2y3 = -2xy2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 2y3 = -2xy2 + -1x3
2y3 = -2xy2 + -1x3

Add '-2y3' to each side of the equation.
2y3 + -2y3 = -2xy2 + -1x3 + -2y3

Combine like terms: 2y3 + -2y3 = 0
0 = -2xy2 + -1x3 + -2y3

Simplifying
0 = -2xy2 + -1x3 + -2y3

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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