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

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


Simplifying
(3x2 + 2xy + 2y2) * dx + (x2 + 4xy + 2y2) * dy = 0

Reorder the terms:
(2xy + 3x2 + 2y2) * dx + (x2 + 4xy + 2y2) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + 3x2 + 2y2) + (x2 + 4xy + 2y2) * dy = 0
(2xy * dx + 3x2 * dx + 2y2 * dx) + (x2 + 4xy + 2y2) * dy = 0

Reorder the terms:
(2dxy2 + 2dx2y + 3dx3) + (x2 + 4xy + 2y2) * dy = 0
(2dxy2 + 2dx2y + 3dx3) + (x2 + 4xy + 2y2) * dy = 0

Reorder the terms:
2dxy2 + 2dx2y + 3dx3 + (4xy + x2 + 2y2) * dy = 0

Reorder the terms for easier multiplication:
2dxy2 + 2dx2y + 3dx3 + dy(4xy + x2 + 2y2) = 0
2dxy2 + 2dx2y + 3dx3 + (4xy * dy + x2 * dy + 2y2 * dy) = 0
2dxy2 + 2dx2y + 3dx3 + (4dxy2 + dx2y + 2dy3) = 0

Reorder the terms:
2dxy2 + 4dxy2 + 2dx2y + dx2y + 3dx3 + 2dy3 = 0

Combine like terms: 2dxy2 + 4dxy2 = 6dxy2
6dxy2 + 2dx2y + dx2y + 3dx3 + 2dy3 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
6dxy2 + 3dx2y + 3dx3 + 2dy3 = 0

Solving
6dxy2 + 3dx2y + 3dx3 + 2dy3 = 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(6xy2 + 3x2y + 3x3 + 2y3) = 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 '(6xy2 + 3x2y + 3x3 + 2y3)' equal to zero and attempt to solve:

Simplifying
6xy2 + 3x2y + 3x3 + 2y3 = 0

Solving
6xy2 + 3x2y + 3x3 + 2y3 = 0

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

Add '-6xy2' to each side of the equation.
6xy2 + 3x2y + 3x3 + -6xy2 + 2y3 = 0 + -6xy2

Reorder the terms:
6xy2 + -6xy2 + 3x2y + 3x3 + 2y3 = 0 + -6xy2

Combine like terms: 6xy2 + -6xy2 = 0
0 + 3x2y + 3x3 + 2y3 = 0 + -6xy2
3x2y + 3x3 + 2y3 = 0 + -6xy2
Remove the zero:
3x2y + 3x3 + 2y3 = -6xy2

Add '-3x2y' to each side of the equation.
3x2y + 3x3 + -3x2y + 2y3 = -6xy2 + -3x2y

Reorder the terms:
3x2y + -3x2y + 3x3 + 2y3 = -6xy2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 3x3 + 2y3 = -6xy2 + -3x2y
3x3 + 2y3 = -6xy2 + -3x2y

Add '-3x3' to each side of the equation.
3x3 + -3x3 + 2y3 = -6xy2 + -3x2y + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 2y3 = -6xy2 + -3x2y + -3x3
2y3 = -6xy2 + -3x2y + -3x3

Add '-2y3' to each side of the equation.
2y3 + -2y3 = -6xy2 + -3x2y + -3x3 + -2y3

Combine like terms: 2y3 + -2y3 = 0
0 = -6xy2 + -3x2y + -3x3 + -2y3

Simplifying
0 = -6xy2 + -3x2y + -3x3 + -2y3

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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