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

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


Simplifying
(3x2y + 6x) * dx + (x3 + 3y2) * dy = 0

Reorder the terms:
(6x + 3x2y) * dx + (x3 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + 3x2y) + (x3 + 3y2) * dy = 0
(6x * dx + 3x2y * dx) + (x3 + 3y2) * dy = 0
(6dx2 + 3dx3y) + (x3 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
6dx2 + 3dx3y + dy(x3 + 3y2) = 0
6dx2 + 3dx3y + (x3 * dy + 3y2 * dy) = 0
6dx2 + 3dx3y + (dx3y + 3dy3) = 0

Combine like terms: 3dx3y + dx3y = 4dx3y
6dx2 + 4dx3y + 3dy3 = 0

Solving
6dx2 + 4dx3y + 3dy3 = 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(6x2 + 4x3y + 3y3) = 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 '(6x2 + 4x3y + 3y3)' equal to zero and attempt to solve:

Simplifying
6x2 + 4x3y + 3y3 = 0

Solving
6x2 + 4x3y + 3y3 = 0

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

Add '-6x2' to each side of the equation.
6x2 + 4x3y + -6x2 + 3y3 = 0 + -6x2

Reorder the terms:
6x2 + -6x2 + 4x3y + 3y3 = 0 + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + 4x3y + 3y3 = 0 + -6x2
4x3y + 3y3 = 0 + -6x2
Remove the zero:
4x3y + 3y3 = -6x2

Add '-4x3y' to each side of the equation.
4x3y + -4x3y + 3y3 = -6x2 + -4x3y

Combine like terms: 4x3y + -4x3y = 0
0 + 3y3 = -6x2 + -4x3y
3y3 = -6x2 + -4x3y

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -6x2 + -4x3y + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -6x2 + -4x3y + -3y3

Simplifying
0 = -6x2 + -4x3y + -3y3

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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