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

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


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

Reorder the terms for easier multiplication:
dx(3x + 4xy) + (2x + 2y) * dy = 0
(3x * dx + 4xy * dx) + (2x + 2y) * dy = 0
(3dx2 + 4dx2y) + (2x + 2y) * dy = 0

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

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

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

Simplifying
2xy + 3x2 + 4x2y + 2y2 = 0

Solving
2xy + 3x2 + 4x2y + 2y2 = 0

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -2xy + -3x2 + -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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