(3x^2-4xy^2)dx+(x^3-4x^2+12y^3)dy=0

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Solution for (3x^2-4xy^2)dx+(x^3-4x^2+12y^3)dy=0 equation: 


Simplifying
(3x2 + -4xy2) * dx + (x3 + -4x2 + 12y3) * dy = 0

Reorder the terms:
(-4xy2 + 3x2) * dx + (x3 + -4x2 + 12y3) * dy = 0

Reorder the terms for easier multiplication:
dx(-4xy2 + 3x2) + (x3 + -4x2 + 12y3) * dy = 0
(-4xy2 * dx + 3x2 * dx) + (x3 + -4x2 + 12y3) * dy = 0
(-4dx2y2 + 3dx3) + (x3 + -4x2 + 12y3) * dy = 0

Reorder the terms:
-4dx2y2 + 3dx3 + (-4x2 + x3 + 12y3) * dy = 0

Reorder the terms for easier multiplication:
-4dx2y2 + 3dx3 + dy(-4x2 + x3 + 12y3) = 0
-4dx2y2 + 3dx3 + (-4x2 * dy + x3 * dy + 12y3 * dy) = 0
-4dx2y2 + 3dx3 + (-4dx2y + dx3y + 12dy4) = 0

Reorder the terms:
-4dx2y + -4dx2y2 + 3dx3 + dx3y + 12dy4 = 0

Solving
-4dx2y + -4dx2y2 + 3dx3 + dx3y + 12dy4 = 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(-4x2y + -4x2y2 + 3x3 + x3y + 12y4) = 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 '(-4x2y + -4x2y2 + 3x3 + x3y + 12y4)' equal to zero and attempt to solve:

Simplifying
-4x2y + -4x2y2 + 3x3 + x3y + 12y4 = 0

Solving
-4x2y + -4x2y2 + 3x3 + x3y + 12y4 = 0

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

Add '4x2y' to each side of the equation.
-4x2y + -4x2y2 + 3x3 + x3y + 4x2y + 12y4 = 0 + 4x2y

Reorder the terms:
-4x2y + 4x2y + -4x2y2 + 3x3 + x3y + 12y4 = 0 + 4x2y

Combine like terms: -4x2y + 4x2y = 0
0 + -4x2y2 + 3x3 + x3y + 12y4 = 0 + 4x2y
-4x2y2 + 3x3 + x3y + 12y4 = 0 + 4x2y
Remove the zero:
-4x2y2 + 3x3 + x3y + 12y4 = 4x2y

Add '4x2y2' to each side of the equation.
-4x2y2 + 3x3 + x3y + 4x2y2 + 12y4 = 4x2y + 4x2y2

Reorder the terms:
-4x2y2 + 4x2y2 + 3x3 + x3y + 12y4 = 4x2y + 4x2y2

Combine like terms: -4x2y2 + 4x2y2 = 0
0 + 3x3 + x3y + 12y4 = 4x2y + 4x2y2
3x3 + x3y + 12y4 = 4x2y + 4x2y2

Add '-3x3' to each side of the equation.
3x3 + x3y + -3x3 + 12y4 = 4x2y + 4x2y2 + -3x3

Reorder the terms:
3x3 + -3x3 + x3y + 12y4 = 4x2y + 4x2y2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + x3y + 12y4 = 4x2y + 4x2y2 + -3x3
x3y + 12y4 = 4x2y + 4x2y2 + -3x3

Add '-1x3y' to each side of the equation.
x3y + -1x3y + 12y4 = 4x2y + 4x2y2 + -3x3 + -1x3y

Combine like terms: x3y + -1x3y = 0
0 + 12y4 = 4x2y + 4x2y2 + -3x3 + -1x3y
12y4 = 4x2y + 4x2y2 + -3x3 + -1x3y

Add '-12y4' to each side of the equation.
12y4 + -12y4 = 4x2y + 4x2y2 + -3x3 + -1x3y + -12y4

Combine like terms: 12y4 + -12y4 = 0
0 = 4x2y + 4x2y2 + -3x3 + -1x3y + -12y4

Simplifying
0 = 4x2y + 4x2y2 + -3x3 + -1x3y + -12y4

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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