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

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


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

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

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

Reorder the terms:
(dxy2 + 3dx2y + 4dx3) + (4y2 + 3xy + x2) * dy = 0
(dxy2 + 3dx2y + 4dx3) + (4y2 + 3xy + x2) * dy = 0

Reorder the terms:
dxy2 + 3dx2y + 4dx3 + (3xy + x2 + 4y2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 3dx2y + 4dx3 + dy(3xy + x2 + 4y2) = 0
dxy2 + 3dx2y + 4dx3 + (3xy * dy + x2 * dy + 4y2 * dy) = 0
dxy2 + 3dx2y + 4dx3 + (3dxy2 + dx2y + 4dy3) = 0

Reorder the terms:
dxy2 + 3dxy2 + 3dx2y + dx2y + 4dx3 + 4dy3 = 0

Combine like terms: dxy2 + 3dxy2 = 4dxy2
4dxy2 + 3dx2y + dx2y + 4dx3 + 4dy3 = 0

Combine like terms: 3dx2y + dx2y = 4dx2y
4dxy2 + 4dx2y + 4dx3 + 4dy3 = 0

Solving
4dxy2 + 4dx2y + 4dx3 + 4dy3 = 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), '4d'.
4d(xy2 + x2y + x3 + y3) = 0

Ignore the factor 4.

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 '(xy2 + x2y + x3 + y3)' equal to zero and attempt to solve:

Simplifying
xy2 + x2y + x3 + y3 = 0

Solving
xy2 + x2y + x3 + y3 = 0

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

Add '-1xy2' to each side of the equation.
xy2 + x2y + x3 + -1xy2 + y3 = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + x2y + x3 + y3 = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2y + x3 + y3 = 0 + -1xy2
x2y + x3 + y3 = 0 + -1xy2
Remove the zero:
x2y + x3 + y3 = -1xy2

Add '-1x2y' to each side of the equation.
x2y + x3 + -1x2y + y3 = -1xy2 + -1x2y

Reorder the terms:
x2y + -1x2y + x3 + y3 = -1xy2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + x3 + y3 = -1xy2 + -1x2y
x3 + y3 = -1xy2 + -1x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + y3 = -1xy2 + -1x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y3 = -1xy2 + -1x2y + -1x3
y3 = -1xy2 + -1x2y + -1x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1xy2 + -1x2y + -1x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1xy2 + -1x2y + -1x3 + -1y3

Simplifying
0 = -1xy2 + -1x2y + -1x3 + -1y3

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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