(3x^2+2y+1)dx+(2x+6y^2+2)dy=0

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Solution for (3x^2+2y+1)dx+(2x+6y^2+2)dy=0 equation: 


Simplifying
(3x2 + 2y + 1) * dx + (2x + 6y2 + 2) * dy = 0

Reorder the terms:
(1 + 3x2 + 2y) * dx + (2x + 6y2 + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 3x2 + 2y) + (2x + 6y2 + 2) * dy = 0
(1 * dx + 3x2 * dx + 2y * dx) + (2x + 6y2 + 2) * dy = 0

Reorder the terms:
(1dx + 2dxy + 3dx3) + (2x + 6y2 + 2) * dy = 0
(1dx + 2dxy + 3dx3) + (2x + 6y2 + 2) * dy = 0

Reorder the terms:
1dx + 2dxy + 3dx3 + (2 + 2x + 6y2) * dy = 0

Reorder the terms for easier multiplication:
1dx + 2dxy + 3dx3 + dy(2 + 2x + 6y2) = 0
1dx + 2dxy + 3dx3 + (2 * dy + 2x * dy + 6y2 * dy) = 0

Reorder the terms:
1dx + 2dxy + 3dx3 + (2dxy + 2dy + 6dy3) = 0
1dx + 2dxy + 3dx3 + (2dxy + 2dy + 6dy3) = 0

Reorder the terms:
1dx + 2dxy + 2dxy + 3dx3 + 2dy + 6dy3 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
1dx + 4dxy + 3dx3 + 2dy + 6dy3 = 0

Solving
1dx + 4dxy + 3dx3 + 2dy + 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), 'd'.
d(x + 4xy + 3x3 + 2y + 6y3) = 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 '(x + 4xy + 3x3 + 2y + 6y3)' equal to zero and attempt to solve:

Simplifying
x + 4xy + 3x3 + 2y + 6y3 = 0

Solving
x + 4xy + 3x3 + 2y + 6y3 = 0

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

Add '-1x' to each side of the equation.
x + 4xy + 3x3 + 2y + -1x + 6y3 = 0 + -1x

Reorder the terms:
x + -1x + 4xy + 3x3 + 2y + 6y3 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 4xy + 3x3 + 2y + 6y3 = 0 + -1x
4xy + 3x3 + 2y + 6y3 = 0 + -1x
Remove the zero:
4xy + 3x3 + 2y + 6y3 = -1x

Add '-4xy' to each side of the equation.
4xy + 3x3 + 2y + -4xy + 6y3 = -1x + -4xy

Reorder the terms:
4xy + -4xy + 3x3 + 2y + 6y3 = -1x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3x3 + 2y + 6y3 = -1x + -4xy
3x3 + 2y + 6y3 = -1x + -4xy

Add '-3x3' to each side of the equation.
3x3 + 2y + -3x3 + 6y3 = -1x + -4xy + -3x3

Reorder the terms:
3x3 + -3x3 + 2y + 6y3 = -1x + -4xy + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 2y + 6y3 = -1x + -4xy + -3x3
2y + 6y3 = -1x + -4xy + -3x3

Add '-2y' to each side of the equation.
2y + -2y + 6y3 = -1x + -4xy + -3x3 + -2y

Combine like terms: 2y + -2y = 0
0 + 6y3 = -1x + -4xy + -3x3 + -2y
6y3 = -1x + -4xy + -3x3 + -2y

Add '-6y3' to each side of the equation.
6y3 + -6y3 = -1x + -4xy + -3x3 + -2y + -6y3

Combine like terms: 6y3 + -6y3 = 0
0 = -1x + -4xy + -3x3 + -2y + -6y3

Simplifying
0 = -1x + -4xy + -3x3 + -2y + -6y3

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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