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

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


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

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

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

Reorder the terms for easier multiplication:
-6dx2y + 3dx3 + -1dy(3x2 + 2y) = 0
-6dx2y + 3dx3 + (3x2 * -1dy + 2y * -1dy) = 0
-6dx2y + 3dx3 + (-3dx2y + -2dy2) = 0

Reorder the terms:
-6dx2y + -3dx2y + 3dx3 + -2dy2 = 0

Combine like terms: -6dx2y + -3dx2y = -9dx2y
-9dx2y + 3dx3 + -2dy2 = 0

Solving
-9dx2y + 3dx3 + -2dy2 = 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(-9x2y + 3x3 + -2y2) = 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 '(-9x2y + 3x3 + -2y2)' equal to zero and attempt to solve:

Simplifying
-9x2y + 3x3 + -2y2 = 0

Solving
-9x2y + 3x3 + -2y2 = 0

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

Add '9x2y' to each side of the equation.
-9x2y + 3x3 + 9x2y + -2y2 = 0 + 9x2y

Reorder the terms:
-9x2y + 9x2y + 3x3 + -2y2 = 0 + 9x2y

Combine like terms: -9x2y + 9x2y = 0
0 + 3x3 + -2y2 = 0 + 9x2y
3x3 + -2y2 = 0 + 9x2y
Remove the zero:
3x3 + -2y2 = 9x2y

Add '-3x3' to each side of the equation.
3x3 + -3x3 + -2y2 = 9x2y + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + -2y2 = 9x2y + -3x3
-2y2 = 9x2y + -3x3

Add '2y2' to each side of the equation.
-2y2 + 2y2 = 9x2y + -3x3 + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = 9x2y + -3x3 + 2y2

Simplifying
0 = 9x2y + -3x3 + 2y2

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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