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

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


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

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

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

Reorder the terms for easier multiplication:
-6dx2y + 6dx3 + dy(-3x2 + -3y2) = 0
-6dx2y + 6dx3 + (-3x2 * dy + -3y2 * dy) = 0
-6dx2y + 6dx3 + (-3dx2y + -3dy3) = 0

Reorder the terms:
-6dx2y + -3dx2y + 6dx3 + -3dy3 = 0

Combine like terms: -6dx2y + -3dx2y = -9dx2y
-9dx2y + 6dx3 + -3dy3 = 0

Solving
-9dx2y + 6dx3 + -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), '3d'.
3d(-3x2y + 2x3 + -1y3) = 0

Ignore the factor 3.

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 '(-3x2y + 2x3 + -1y3)' equal to zero and attempt to solve:

Simplifying
-3x2y + 2x3 + -1y3 = 0

Solving
-3x2y + 2x3 + -1y3 = 0

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

Add '3x2y' to each side of the equation.
-3x2y + 2x3 + 3x2y + -1y3 = 0 + 3x2y

Reorder the terms:
-3x2y + 3x2y + 2x3 + -1y3 = 0 + 3x2y

Combine like terms: -3x2y + 3x2y = 0
0 + 2x3 + -1y3 = 0 + 3x2y
2x3 + -1y3 = 0 + 3x2y
Remove the zero:
2x3 + -1y3 = 3x2y

Add '-2x3' to each side of the equation.
2x3 + -2x3 + -1y3 = 3x2y + -2x3

Combine like terms: 2x3 + -2x3 = 0
0 + -1y3 = 3x2y + -2x3
-1y3 = 3x2y + -2x3

Add 'y3' to each side of the equation.
-1y3 + y3 = 3x2y + -2x3 + y3

Combine like terms: -1y3 + y3 = 0
0 = 3x2y + -2x3 + y3

Simplifying
0 = 3x2y + -2x3 + y3

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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