(3x^2+8x^3y)dx+(2y+2x^4)dy=0

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Solution for (3x^2+8x^3y)dx+(2y+2x^4)dy=0 equation: 


Simplifying
(3x2 + 8x3y) * dx + (2y + 2x4) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + 8x3y) + (2y + 2x4) * dy = 0
(3x2 * dx + 8x3y * dx) + (2y + 2x4) * dy = 0
(3dx3 + 8dx4y) + (2y + 2x4) * dy = 0

Reorder the terms:
3dx3 + 8dx4y + (2x4 + 2y) * dy = 0

Reorder the terms for easier multiplication:
3dx3 + 8dx4y + dy(2x4 + 2y) = 0
3dx3 + 8dx4y + (2x4 * dy + 2y * dy) = 0
3dx3 + 8dx4y + (2dx4y + 2dy2) = 0

Combine like terms: 8dx4y + 2dx4y = 10dx4y
3dx3 + 10dx4y + 2dy2 = 0

Solving
3dx3 + 10dx4y + 2dy2 = 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(3x3 + 10x4y + 2y2) = 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 '(3x3 + 10x4y + 2y2)' equal to zero and attempt to solve:

Simplifying
3x3 + 10x4y + 2y2 = 0

Solving
3x3 + 10x4y + 2y2 = 0

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

Add '-3x3' to each side of the equation.
3x3 + 10x4y + -3x3 + 2y2 = 0 + -3x3

Reorder the terms:
3x3 + -3x3 + 10x4y + 2y2 = 0 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 10x4y + 2y2 = 0 + -3x3
10x4y + 2y2 = 0 + -3x3
Remove the zero:
10x4y + 2y2 = -3x3

Add '-10x4y' to each side of the equation.
10x4y + -10x4y + 2y2 = -3x3 + -10x4y

Combine like terms: 10x4y + -10x4y = 0
0 + 2y2 = -3x3 + -10x4y
2y2 = -3x3 + -10x4y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -3x3 + -10x4y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -3x3 + -10x4y + -2y2

Simplifying
0 = -3x3 + -10x4y + -2y2

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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