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

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


Simplifying
(3xy2 + -1x2) * dx + (3x2y + -6y2 + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(3xy2 + -1x2) + (3x2y + -6y2 + -1) * dy = 0
(3xy2 * dx + -1x2 * dx) + (3x2y + -6y2 + -1) * dy = 0
(3dx2y2 + -1dx3) + (3x2y + -6y2 + -1) * dy = 0

Reorder the terms:
3dx2y2 + -1dx3 + (-1 + 3x2y + -6y2) * dy = 0

Reorder the terms for easier multiplication:
3dx2y2 + -1dx3 + dy(-1 + 3x2y + -6y2) = 0
3dx2y2 + -1dx3 + (-1 * dy + 3x2y * dy + -6y2 * dy) = 0

Reorder the terms:
3dx2y2 + -1dx3 + (3dx2y2 + -1dy + -6dy3) = 0
3dx2y2 + -1dx3 + (3dx2y2 + -1dy + -6dy3) = 0

Reorder the terms:
3dx2y2 + 3dx2y2 + -1dx3 + -1dy + -6dy3 = 0

Combine like terms: 3dx2y2 + 3dx2y2 = 6dx2y2
6dx2y2 + -1dx3 + -1dy + -6dy3 = 0

Solving
6dx2y2 + -1dx3 + -1dy + -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(6x2y2 + -1x3 + -1y + -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 '(6x2y2 + -1x3 + -1y + -6y3)' equal to zero and attempt to solve:

Simplifying
6x2y2 + -1x3 + -1y + -6y3 = 0

Solving
6x2y2 + -1x3 + -1y + -6y3 = 0

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

Add '-6x2y2' to each side of the equation.
6x2y2 + -1x3 + -1y + -6x2y2 + -6y3 = 0 + -6x2y2

Reorder the terms:
6x2y2 + -6x2y2 + -1x3 + -1y + -6y3 = 0 + -6x2y2

Combine like terms: 6x2y2 + -6x2y2 = 0
0 + -1x3 + -1y + -6y3 = 0 + -6x2y2
-1x3 + -1y + -6y3 = 0 + -6x2y2
Remove the zero:
-1x3 + -1y + -6y3 = -6x2y2

Add 'x3' to each side of the equation.
-1x3 + -1y + x3 + -6y3 = -6x2y2 + x3

Reorder the terms:
-1x3 + x3 + -1y + -6y3 = -6x2y2 + x3

Combine like terms: -1x3 + x3 = 0
0 + -1y + -6y3 = -6x2y2 + x3
-1y + -6y3 = -6x2y2 + x3

Add 'y' to each side of the equation.
-1y + y + -6y3 = -6x2y2 + x3 + y

Combine like terms: -1y + y = 0
0 + -6y3 = -6x2y2 + x3 + y
-6y3 = -6x2y2 + x3 + y

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

Combine like terms: -6y3 + 6y3 = 0
0 = -6x2y2 + x3 + y + 6y3

Simplifying
0 = -6x2y2 + x3 + y + 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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