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

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


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

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

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

Reorder the terms:
(3dxy + 2dx2 + 2dx2y) + (6xy + x * x + 3) * dy = 0
(3dxy + 2dx2 + 2dx2y) + (6xy + x * x + 3) * dy = 0

Multiply x * x
3dxy + 2dx2 + 2dx2y + (6xy + x2 + 3) * dy = 0

Reorder the terms:
3dxy + 2dx2 + 2dx2y + (3 + 6xy + x2) * dy = 0

Reorder the terms for easier multiplication:
3dxy + 2dx2 + 2dx2y + dy(3 + 6xy + x2) = 0
3dxy + 2dx2 + 2dx2y + (3 * dy + 6xy * dy + x2 * dy) = 0

Reorder the terms:
3dxy + 2dx2 + 2dx2y + (6dxy2 + dx2y + 3dy) = 0
3dxy + 2dx2 + 2dx2y + (6dxy2 + dx2y + 3dy) = 0

Reorder the terms:
3dxy + 6dxy2 + 2dx2 + 2dx2y + dx2y + 3dy = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
3dxy + 6dxy2 + 2dx2 + 3dx2y + 3dy = 0

Solving
3dxy + 6dxy2 + 2dx2 + 3dx2y + 3dy = 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(3xy + 6xy2 + 2x2 + 3x2y + 3y) = 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 '(3xy + 6xy2 + 2x2 + 3x2y + 3y)' equal to zero and attempt to solve:

Simplifying
3xy + 6xy2 + 2x2 + 3x2y + 3y = 0

Solving
3xy + 6xy2 + 2x2 + 3x2y + 3y = 0

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

Add '-3xy' to each side of the equation.
3xy + 6xy2 + 2x2 + 3x2y + -3xy + 3y = 0 + -3xy

Reorder the terms:
3xy + -3xy + 6xy2 + 2x2 + 3x2y + 3y = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + 6xy2 + 2x2 + 3x2y + 3y = 0 + -3xy
6xy2 + 2x2 + 3x2y + 3y = 0 + -3xy
Remove the zero:
6xy2 + 2x2 + 3x2y + 3y = -3xy

Add '-6xy2' to each side of the equation.
6xy2 + 2x2 + 3x2y + -6xy2 + 3y = -3xy + -6xy2

Reorder the terms:
6xy2 + -6xy2 + 2x2 + 3x2y + 3y = -3xy + -6xy2

Combine like terms: 6xy2 + -6xy2 = 0
0 + 2x2 + 3x2y + 3y = -3xy + -6xy2
2x2 + 3x2y + 3y = -3xy + -6xy2

Add '-2x2' to each side of the equation.
2x2 + 3x2y + -2x2 + 3y = -3xy + -6xy2 + -2x2

Reorder the terms:
2x2 + -2x2 + 3x2y + 3y = -3xy + -6xy2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 3x2y + 3y = -3xy + -6xy2 + -2x2
3x2y + 3y = -3xy + -6xy2 + -2x2

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + 3y = -3xy + -6xy2 + -2x2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 3y = -3xy + -6xy2 + -2x2 + -3x2y
3y = -3xy + -6xy2 + -2x2 + -3x2y

Add '-3y' to each side of the equation.
3y + -3y = -3xy + -6xy2 + -2x2 + -3x2y + -3y

Combine like terms: 3y + -3y = 0
0 = -3xy + -6xy2 + -2x2 + -3x2y + -3y

Simplifying
0 = -3xy + -6xy2 + -2x2 + -3x2y + -3y

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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