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

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


Simplifying
(3x2 + 3xy2) * dx + (3x2y + -3y2 + 2y) * dy = 0

Reorder the terms:
(3xy2 + 3x2) * dx + (3x2y + -3y2 + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx(3xy2 + 3x2) + (3x2y + -3y2 + 2y) * dy = 0
(3xy2 * dx + 3x2 * dx) + (3x2y + -3y2 + 2y) * dy = 0
(3dx2y2 + 3dx3) + (3x2y + -3y2 + 2y) * dy = 0

Reorder the terms:
3dx2y2 + 3dx3 + (3x2y + 2y + -3y2) * dy = 0

Reorder the terms for easier multiplication:
3dx2y2 + 3dx3 + dy(3x2y + 2y + -3y2) = 0
3dx2y2 + 3dx3 + (3x2y * dy + 2y * dy + -3y2 * dy) = 0
3dx2y2 + 3dx3 + (3dx2y2 + 2dy2 + -3dy3) = 0

Reorder the terms:
3dx2y2 + 3dx2y2 + 3dx3 + 2dy2 + -3dy3 = 0

Combine like terms: 3dx2y2 + 3dx2y2 = 6dx2y2
6dx2y2 + 3dx3 + 2dy2 + -3dy3 = 0

Solving
6dx2y2 + 3dx3 + 2dy2 + -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(6x2y2 + 3x3 + 2y2 + -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 '(6x2y2 + 3x3 + 2y2 + -3y3)' equal to zero and attempt to solve:

Simplifying
6x2y2 + 3x3 + 2y2 + -3y3 = 0

Solving
6x2y2 + 3x3 + 2y2 + -3y3 = 0

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

Add '-6x2y2' to each side of the equation.
6x2y2 + 3x3 + 2y2 + -6x2y2 + -3y3 = 0 + -6x2y2

Reorder the terms:
6x2y2 + -6x2y2 + 3x3 + 2y2 + -3y3 = 0 + -6x2y2

Combine like terms: 6x2y2 + -6x2y2 = 0
0 + 3x3 + 2y2 + -3y3 = 0 + -6x2y2
3x3 + 2y2 + -3y3 = 0 + -6x2y2
Remove the zero:
3x3 + 2y2 + -3y3 = -6x2y2

Add '-3x3' to each side of the equation.
3x3 + 2y2 + -3x3 + -3y3 = -6x2y2 + -3x3

Reorder the terms:
3x3 + -3x3 + 2y2 + -3y3 = -6x2y2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 2y2 + -3y3 = -6x2y2 + -3x3
2y2 + -3y3 = -6x2y2 + -3x3

Add '-2y2' to each side of the equation.
2y2 + -2y2 + -3y3 = -6x2y2 + -3x3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 + -3y3 = -6x2y2 + -3x3 + -2y2
-3y3 = -6x2y2 + -3x3 + -2y2

Add '3y3' to each side of the equation.
-3y3 + 3y3 = -6x2y2 + -3x3 + -2y2 + 3y3

Combine like terms: -3y3 + 3y3 = 0
0 = -6x2y2 + -3x3 + -2y2 + 3y3

Simplifying
0 = -6x2y2 + -3x3 + -2y2 + 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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