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

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


Simplifying
(3x2 + -2xy + 2) * dx + (6y2 + -1x2 + 3) * dy = 0

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

Reorder the terms for easier multiplication:
dx(2 + -2xy + 3x2) + (6y2 + -1x2 + 3) * dy = 0
(2 * dx + -2xy * dx + 3x2 * dx) + (6y2 + -1x2 + 3) * dy = 0
(2dx + -2dx2y + 3dx3) + (6y2 + -1x2 + 3) * dy = 0

Reorder the terms:
2dx + -2dx2y + 3dx3 + (3 + -1x2 + 6y2) * dy = 0

Reorder the terms for easier multiplication:
2dx + -2dx2y + 3dx3 + dy(3 + -1x2 + 6y2) = 0
2dx + -2dx2y + 3dx3 + (3 * dy + -1x2 * dy + 6y2 * dy) = 0

Reorder the terms:
2dx + -2dx2y + 3dx3 + (-1dx2y + 3dy + 6dy3) = 0
2dx + -2dx2y + 3dx3 + (-1dx2y + 3dy + 6dy3) = 0

Reorder the terms:
2dx + -2dx2y + -1dx2y + 3dx3 + 3dy + 6dy3 = 0

Combine like terms: -2dx2y + -1dx2y = -3dx2y
2dx + -3dx2y + 3dx3 + 3dy + 6dy3 = 0

Solving
2dx + -3dx2y + 3dx3 + 3dy + 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(2x + -3x2y + 3x3 + 3y + 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 '(2x + -3x2y + 3x3 + 3y + 6y3)' equal to zero and attempt to solve:

Simplifying
2x + -3x2y + 3x3 + 3y + 6y3 = 0

Solving
2x + -3x2y + 3x3 + 3y + 6y3 = 0

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

Add '-2x' to each side of the equation.
2x + -3x2y + 3x3 + 3y + -2x + 6y3 = 0 + -2x

Reorder the terms:
2x + -2x + -3x2y + 3x3 + 3y + 6y3 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -3x2y + 3x3 + 3y + 6y3 = 0 + -2x
-3x2y + 3x3 + 3y + 6y3 = 0 + -2x
Remove the zero:
-3x2y + 3x3 + 3y + 6y3 = -2x

Add '3x2y' to each side of the equation.
-3x2y + 3x3 + 3y + 3x2y + 6y3 = -2x + 3x2y

Reorder the terms:
-3x2y + 3x2y + 3x3 + 3y + 6y3 = -2x + 3x2y

Combine like terms: -3x2y + 3x2y = 0
0 + 3x3 + 3y + 6y3 = -2x + 3x2y
3x3 + 3y + 6y3 = -2x + 3x2y

Add '-3x3' to each side of the equation.
3x3 + 3y + -3x3 + 6y3 = -2x + 3x2y + -3x3

Reorder the terms:
3x3 + -3x3 + 3y + 6y3 = -2x + 3x2y + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 3y + 6y3 = -2x + 3x2y + -3x3
3y + 6y3 = -2x + 3x2y + -3x3

Add '-3y' to each side of the equation.
3y + -3y + 6y3 = -2x + 3x2y + -3x3 + -3y

Combine like terms: 3y + -3y = 0
0 + 6y3 = -2x + 3x2y + -3x3 + -3y
6y3 = -2x + 3x2y + -3x3 + -3y

Add '-6y3' to each side of the equation.
6y3 + -6y3 = -2x + 3x2y + -3x3 + -3y + -6y3

Combine like terms: 6y3 + -6y3 = 0
0 = -2x + 3x2y + -3x3 + -3y + -6y3

Simplifying
0 = -2x + 3x2y + -3x3 + -3y + -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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