(3x+6y)dx+(6x-8y^3)dy=0

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Solution for (3x+6y)dx+(6x-8y^3)dy=0 equation: 


Simplifying
(3x + 6y) * dx + (6x + -8y3) * dy = 0

Reorder the terms for easier multiplication:
dx(3x + 6y) + (6x + -8y3) * dy = 0
(3x * dx + 6y * dx) + (6x + -8y3) * dy = 0

Reorder the terms:
(6dxy + 3dx2) + (6x + -8y3) * dy = 0
(6dxy + 3dx2) + (6x + -8y3) * dy = 0

Reorder the terms for easier multiplication:
6dxy + 3dx2 + dy(6x + -8y3) = 0
6dxy + 3dx2 + (6x * dy + -8y3 * dy) = 0
6dxy + 3dx2 + (6dxy + -8dy4) = 0

Reorder the terms:
6dxy + 6dxy + 3dx2 + -8dy4 = 0

Combine like terms: 6dxy + 6dxy = 12dxy
12dxy + 3dx2 + -8dy4 = 0

Solving
12dxy + 3dx2 + -8dy4 = 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(12xy + 3x2 + -8y4) = 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 '(12xy + 3x2 + -8y4)' equal to zero and attempt to solve:

Simplifying
12xy + 3x2 + -8y4 = 0

Solving
12xy + 3x2 + -8y4 = 0

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

Add '-12xy' to each side of the equation.
12xy + 3x2 + -12xy + -8y4 = 0 + -12xy

Reorder the terms:
12xy + -12xy + 3x2 + -8y4 = 0 + -12xy

Combine like terms: 12xy + -12xy = 0
0 + 3x2 + -8y4 = 0 + -12xy
3x2 + -8y4 = 0 + -12xy
Remove the zero:
3x2 + -8y4 = -12xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + -8y4 = -12xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -8y4 = -12xy + -3x2
-8y4 = -12xy + -3x2

Add '8y4' to each side of the equation.
-8y4 + 8y4 = -12xy + -3x2 + 8y4

Combine like terms: -8y4 + 8y4 = 0
0 = -12xy + -3x2 + 8y4

Simplifying
0 = -12xy + -3x2 + 8y4

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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