(24x^2+8xy^2)dx+(8y^2-8x^2y)dy=0

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Solution for (24x^2+8xy^2)dx+(8y^2-8x^2y)dy=0 equation: 


Simplifying
(24x2 + 8xy2) * dx + (8y2 + -8x2y) * dy = 0

Reorder the terms:
(8xy2 + 24x2) * dx + (8y2 + -8x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(8xy2 + 24x2) + (8y2 + -8x2y) * dy = 0
(8xy2 * dx + 24x2 * dx) + (8y2 + -8x2y) * dy = 0
(8dx2y2 + 24dx3) + (8y2 + -8x2y) * dy = 0

Reorder the terms:
8dx2y2 + 24dx3 + (-8x2y + 8y2) * dy = 0

Reorder the terms for easier multiplication:
8dx2y2 + 24dx3 + dy(-8x2y + 8y2) = 0
8dx2y2 + 24dx3 + (-8x2y * dy + 8y2 * dy) = 0
8dx2y2 + 24dx3 + (-8dx2y2 + 8dy3) = 0

Reorder the terms:
8dx2y2 + -8dx2y2 + 24dx3 + 8dy3 = 0

Combine like terms: 8dx2y2 + -8dx2y2 = 0
0 + 24dx3 + 8dy3 = 0
24dx3 + 8dy3 = 0

Solving
24dx3 + 8dy3 = 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), '8d'.
8d(3x3 + y3) = 0

Ignore the factor 8.

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 '(3x3 + y3)' equal to zero and attempt to solve:

Simplifying
3x3 + y3 = 0

Solving
3x3 + y3 = 0

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

Add '-3x3' to each side of the equation.
3x3 + -3x3 + y3 = 0 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + y3 = 0 + -3x3
y3 = 0 + -3x3
Remove the zero:
y3 = -3x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -3x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -3x3 + -1y3

Simplifying
0 = -3x3 + -1y3

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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