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

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


Simplifying
(3x2 + 3y2) * dx + (x3 + 3xy2 + 6xy) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + 3y2) + (x3 + 3xy2 + 6xy) * dy = 0
(3x2 * dx + 3y2 * dx) + (x3 + 3xy2 + 6xy) * dy = 0

Reorder the terms:
(3dxy2 + 3dx3) + (x3 + 3xy2 + 6xy) * dy = 0
(3dxy2 + 3dx3) + (x3 + 3xy2 + 6xy) * dy = 0

Reorder the terms:
3dxy2 + 3dx3 + (6xy + 3xy2 + x3) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + 3dx3 + dy(6xy + 3xy2 + x3) = 0
3dxy2 + 3dx3 + (6xy * dy + 3xy2 * dy + x3 * dy) = 0
3dxy2 + 3dx3 + (6dxy2 + 3dxy3 + dx3y) = 0

Reorder the terms:
3dxy2 + 6dxy2 + 3dxy3 + 3dx3 + dx3y = 0

Combine like terms: 3dxy2 + 6dxy2 = 9dxy2
9dxy2 + 3dxy3 + 3dx3 + dx3y = 0

Solving
9dxy2 + 3dxy3 + 3dx3 + dx3y = 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), 'dx'.
dx(9y2 + 3y3 + 3x2 + x2y) = 0


Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(9y2 + 3y3 + 3x2 + x2y)' equal to zero and attempt to solve:

Simplifying
9y2 + 3y3 + 3x2 + x2y = 0

Reorder the terms:
3x2 + x2y + 9y2 + 3y3 = 0

Solving
3x2 + x2y + 9y2 + 3y3 = 0

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

Add '-3x2' to each side of the equation.
3x2 + x2y + 9y2 + -3x2 + 3y3 = 0 + -3x2

Reorder the terms:
3x2 + -3x2 + x2y + 9y2 + 3y3 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + x2y + 9y2 + 3y3 = 0 + -3x2
x2y + 9y2 + 3y3 = 0 + -3x2
Remove the zero:
x2y + 9y2 + 3y3 = -3x2

Add '-1x2y' to each side of the equation.
x2y + 9y2 + -1x2y + 3y3 = -3x2 + -1x2y

Reorder the terms:
x2y + -1x2y + 9y2 + 3y3 = -3x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + 9y2 + 3y3 = -3x2 + -1x2y
9y2 + 3y3 = -3x2 + -1x2y

Add '-9y2' to each side of the equation.
9y2 + -9y2 + 3y3 = -3x2 + -1x2y + -9y2

Combine like terms: 9y2 + -9y2 = 0
0 + 3y3 = -3x2 + -1x2y + -9y2
3y3 = -3x2 + -1x2y + -9y2

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -3x2 + -1x2y + -9y2 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -3x2 + -1x2y + -9y2 + -3y3

Simplifying
0 = -3x2 + -1x2y + -9y2 + -3y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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