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

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


Simplifying
(4xy + 3y2 + -1x) * dx + (x + 2y) * dy = 0

Reorder the terms:
(-1x + 4xy + 3y2) * dx + (x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x + 4xy + 3y2) + (x + 2y) * dy = 0
(-1x * dx + 4xy * dx + 3y2 * dx) + (x + 2y) * dy = 0

Reorder the terms:
(3dxy2 + -1dx2 + 4dx2y) + (x + 2y) * dy = 0
(3dxy2 + -1dx2 + 4dx2y) + (x + 2y) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + -1dx2 + 4dx2y + dy(x + 2y) = 0
3dxy2 + -1dx2 + 4dx2y + (x * dy + 2y * dy) = 0
3dxy2 + -1dx2 + 4dx2y + (dxy + 2dy2) = 0

Reorder the terms:
dxy + 3dxy2 + -1dx2 + 4dx2y + 2dy2 = 0

Solving
dxy + 3dxy2 + -1dx2 + 4dx2y + 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(xy + 3xy2 + -1x2 + 4x2y + 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 '(xy + 3xy2 + -1x2 + 4x2y + 2y2)' equal to zero and attempt to solve:

Simplifying
xy + 3xy2 + -1x2 + 4x2y + 2y2 = 0

Solving
xy + 3xy2 + -1x2 + 4x2y + 2y2 = 0

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

Add '-1xy' to each side of the equation.
xy + 3xy2 + -1x2 + 4x2y + -1xy + 2y2 = 0 + -1xy

Reorder the terms:
xy + -1xy + 3xy2 + -1x2 + 4x2y + 2y2 = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + 3xy2 + -1x2 + 4x2y + 2y2 = 0 + -1xy
3xy2 + -1x2 + 4x2y + 2y2 = 0 + -1xy
Remove the zero:
3xy2 + -1x2 + 4x2y + 2y2 = -1xy

Add '-3xy2' to each side of the equation.
3xy2 + -1x2 + 4x2y + -3xy2 + 2y2 = -1xy + -3xy2

Reorder the terms:
3xy2 + -3xy2 + -1x2 + 4x2y + 2y2 = -1xy + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + -1x2 + 4x2y + 2y2 = -1xy + -3xy2
-1x2 + 4x2y + 2y2 = -1xy + -3xy2

Add 'x2' to each side of the equation.
-1x2 + 4x2y + x2 + 2y2 = -1xy + -3xy2 + x2

Reorder the terms:
-1x2 + x2 + 4x2y + 2y2 = -1xy + -3xy2 + x2

Combine like terms: -1x2 + x2 = 0
0 + 4x2y + 2y2 = -1xy + -3xy2 + x2
4x2y + 2y2 = -1xy + -3xy2 + x2

Add '-4x2y' to each side of the equation.
4x2y + -4x2y + 2y2 = -1xy + -3xy2 + x2 + -4x2y

Combine like terms: 4x2y + -4x2y = 0
0 + 2y2 = -1xy + -3xy2 + x2 + -4x2y
2y2 = -1xy + -3xy2 + x2 + -4x2y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1xy + -3xy2 + x2 + -4x2y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1xy + -3xy2 + x2 + -4x2y + -2y2

Simplifying
0 = -1xy + -3xy2 + x2 + -4x2y + -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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