(3x^2+20x^3y^2)dx+(10x^4y-1)dy=0

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Solution for (3x^2+20x^3y^2)dx+(10x^4y-1)dy=0 equation: 


Simplifying
(3x2 + 20x3y2) * dx + (10x4y + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + 20x3y2) + (10x4y + -1) * dy = 0
(3x2 * dx + 20x3y2 * dx) + (10x4y + -1) * dy = 0
(3dx3 + 20dx4y2) + (10x4y + -1) * dy = 0

Reorder the terms:
3dx3 + 20dx4y2 + (-1 + 10x4y) * dy = 0

Reorder the terms for easier multiplication:
3dx3 + 20dx4y2 + dy(-1 + 10x4y) = 0
3dx3 + 20dx4y2 + (-1 * dy + 10x4y * dy) = 0

Reorder the terms:
3dx3 + 20dx4y2 + (10dx4y2 + -1dy) = 0
3dx3 + 20dx4y2 + (10dx4y2 + -1dy) = 0

Combine like terms: 20dx4y2 + 10dx4y2 = 30dx4y2
3dx3 + 30dx4y2 + -1dy = 0

Solving
3dx3 + 30dx4y2 + -1dy = 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 + 30x4y2 + -1y) = 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 + 30x4y2 + -1y)' equal to zero and attempt to solve:

Simplifying
3x3 + 30x4y2 + -1y = 0

Solving
3x3 + 30x4y2 + -1y = 0

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

Add '-3x3' to each side of the equation.
3x3 + 30x4y2 + -3x3 + -1y = 0 + -3x3

Reorder the terms:
3x3 + -3x3 + 30x4y2 + -1y = 0 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 30x4y2 + -1y = 0 + -3x3
30x4y2 + -1y = 0 + -3x3
Remove the zero:
30x4y2 + -1y = -3x3

Add '-30x4y2' to each side of the equation.
30x4y2 + -30x4y2 + -1y = -3x3 + -30x4y2

Combine like terms: 30x4y2 + -30x4y2 = 0
0 + -1y = -3x3 + -30x4y2
-1y = -3x3 + -30x4y2

Add 'y' to each side of the equation.
-1y + y = -3x3 + -30x4y2 + y

Combine like terms: -1y + y = 0
0 = -3x3 + -30x4y2 + y

Simplifying
0 = -3x3 + -30x4y2 + y

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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