(4x^3+6xy)dx+(6x^2y+3y^2)dy=0

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Solution for (4x^3+6xy)dx+(6x^2y+3y^2)dy=0 equation: 


Simplifying
(4x3 + 6xy) * dx + (6x2y + 3y2) * dy = 0

Reorder the terms:
(6xy + 4x3) * dx + (6x2y + 3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(6xy + 4x3) + (6x2y + 3y2) * dy = 0
(6xy * dx + 4x3 * dx) + (6x2y + 3y2) * dy = 0
(6dx2y + 4dx4) + (6x2y + 3y2) * dy = 0

Reorder the terms for easier multiplication:
6dx2y + 4dx4 + dy(6x2y + 3y2) = 0
6dx2y + 4dx4 + (6x2y * dy + 3y2 * dy) = 0
6dx2y + 4dx4 + (6dx2y2 + 3dy3) = 0

Reorder the terms:
6dx2y + 6dx2y2 + 4dx4 + 3dy3 = 0

Solving
6dx2y + 6dx2y2 + 4dx4 + 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), 'd'.
d(6x2y + 6x2y2 + 4x4 + 3y3) = 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 '(6x2y + 6x2y2 + 4x4 + 3y3)' equal to zero and attempt to solve:

Simplifying
6x2y + 6x2y2 + 4x4 + 3y3 = 0

Solving
6x2y + 6x2y2 + 4x4 + 3y3 = 0

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

Add '-6x2y' to each side of the equation.
6x2y + 6x2y2 + 4x4 + -6x2y + 3y3 = 0 + -6x2y

Reorder the terms:
6x2y + -6x2y + 6x2y2 + 4x4 + 3y3 = 0 + -6x2y

Combine like terms: 6x2y + -6x2y = 0
0 + 6x2y2 + 4x4 + 3y3 = 0 + -6x2y
6x2y2 + 4x4 + 3y3 = 0 + -6x2y
Remove the zero:
6x2y2 + 4x4 + 3y3 = -6x2y

Add '-6x2y2' to each side of the equation.
6x2y2 + 4x4 + -6x2y2 + 3y3 = -6x2y + -6x2y2

Reorder the terms:
6x2y2 + -6x2y2 + 4x4 + 3y3 = -6x2y + -6x2y2

Combine like terms: 6x2y2 + -6x2y2 = 0
0 + 4x4 + 3y3 = -6x2y + -6x2y2
4x4 + 3y3 = -6x2y + -6x2y2

Add '-4x4' to each side of the equation.
4x4 + -4x4 + 3y3 = -6x2y + -6x2y2 + -4x4

Combine like terms: 4x4 + -4x4 = 0
0 + 3y3 = -6x2y + -6x2y2 + -4x4
3y3 = -6x2y + -6x2y2 + -4x4

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -6x2y + -6x2y2 + -4x4 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -6x2y + -6x2y2 + -4x4 + -3y3

Simplifying
0 = -6x2y + -6x2y2 + -4x4 + -3y3

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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