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

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


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

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

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

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

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

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

Solving
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(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 '(3x2 + -8y4)' equal to zero and attempt to solve:

Simplifying
3x2 + -8y4 = 0

Solving
3x2 + -8y4 = 0

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

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

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

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

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

Simplifying
0 = -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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