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

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


Simplifying
(3y2 + 4xy) * dx + (4xy + x2) * dy = 0

Reorder the terms:
(4xy + 3y2) * dx + (4xy + x2) * dy = 0

Reorder the terms for easier multiplication:
dx(4xy + 3y2) + (4xy + x2) * dy = 0
(4xy * dx + 3y2 * dx) + (4xy + x2) * dy = 0

Reorder the terms:
(3dxy2 + 4dx2y) + (4xy + x2) * dy = 0
(3dxy2 + 4dx2y) + (4xy + x2) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + 4dx2y + dy(4xy + x2) = 0
3dxy2 + 4dx2y + (4xy * dy + x2 * dy) = 0
3dxy2 + 4dx2y + (4dxy2 + dx2y) = 0

Reorder the terms:
3dxy2 + 4dxy2 + 4dx2y + dx2y = 0

Combine like terms: 3dxy2 + 4dxy2 = 7dxy2
7dxy2 + 4dx2y + dx2y = 0

Combine like terms: 4dx2y + dx2y = 5dx2y
7dxy2 + 5dx2y = 0

Solving
7dxy2 + 5dx2y = 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(7y + 5x) = 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 '(7y + 5x)' equal to zero and attempt to solve:

Simplifying
7y + 5x = 0

Reorder the terms:
5x + 7y = 0

Solving
5x + 7y = 0

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

Add '-5x' to each side of the equation.
5x + -5x + 7y = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 7y = 0 + -5x
7y = 0 + -5x
Remove the zero:
7y = -5x

Add '-7y' to each side of the equation.
7y + -7y = -5x + -7y

Combine like terms: 7y + -7y = 0
0 = -5x + -7y

Simplifying
0 = -5x + -7y

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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