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

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


Simplifying
(4x2y2 + 2y + 2y) * dx + (2x3y + x) * dy = 0

Combine like terms: 2y + 2y = 4y
(4x2y2 + 4y) * dx + (2x3y + x) * dy = 0

Reorder the terms for easier multiplication:
dx(4x2y2 + 4y) + (2x3y + x) * dy = 0
(4x2y2 * dx + 4y * dx) + (2x3y + x) * dy = 0

Reorder the terms:
(4dxy + 4dx3y2) + (2x3y + x) * dy = 0
(4dxy + 4dx3y2) + (2x3y + x) * dy = 0

Reorder the terms:
4dxy + 4dx3y2 + (x + 2x3y) * dy = 0

Reorder the terms for easier multiplication:
4dxy + 4dx3y2 + dy(x + 2x3y) = 0
4dxy + 4dx3y2 + (x * dy + 2x3y * dy) = 0
4dxy + 4dx3y2 + (dxy + 2dx3y2) = 0

Reorder the terms:
4dxy + dxy + 4dx3y2 + 2dx3y2 = 0

Combine like terms: 4dxy + dxy = 5dxy
5dxy + 4dx3y2 + 2dx3y2 = 0

Combine like terms: 4dx3y2 + 2dx3y2 = 6dx3y2
5dxy + 6dx3y2 = 0

Solving
5dxy + 6dx3y2 = 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), 'dxy'.
dxy(5 + 6x2y) = 0


Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve:

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5 + 6x2y)' equal to zero and attempt to solve:

Simplifying
5 + 6x2y = 0

Solving
5 + 6x2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6x2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x2y = 0 + -5
6x2y = 0 + -5

Combine like terms: 0 + -5 = -5
6x2y = -5

Add '-6x2y' to each side of the equation.
6x2y + -6x2y = -5 + -6x2y

Combine like terms: 6x2y + -6x2y = 0
0 = -5 + -6x2y

Simplifying
0 = -5 + -6x2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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