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

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


Simplifying
(2xy + 4y + -3) * dx + (x2 + 4x + 4) * dy = 0

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

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

Reorder the terms:
(-3dx + 4dxy + 2dx2y) + (x2 + 4x + 4) * dy = 0
(-3dx + 4dxy + 2dx2y) + (x2 + 4x + 4) * dy = 0

Reorder the terms:
-3dx + 4dxy + 2dx2y + (4 + 4x + x2) * dy = 0

Reorder the terms for easier multiplication:
-3dx + 4dxy + 2dx2y + dy(4 + 4x + x2) = 0
-3dx + 4dxy + 2dx2y + (4 * dy + 4x * dy + x2 * dy) = 0

Reorder the terms:
-3dx + 4dxy + 2dx2y + (4dxy + dx2y + 4dy) = 0
-3dx + 4dxy + 2dx2y + (4dxy + dx2y + 4dy) = 0

Reorder the terms:
-3dx + 4dxy + 4dxy + 2dx2y + dx2y + 4dy = 0

Combine like terms: 4dxy + 4dxy = 8dxy
-3dx + 8dxy + 2dx2y + dx2y + 4dy = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-3dx + 8dxy + 3dx2y + 4dy = 0

Solving
-3dx + 8dxy + 3dx2y + 4dy = 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(-3x + 8xy + 3x2y + 4y) = 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 '(-3x + 8xy + 3x2y + 4y)' equal to zero and attempt to solve:

Simplifying
-3x + 8xy + 3x2y + 4y = 0

Solving
-3x + 8xy + 3x2y + 4y = 0

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

Add '3x' to each side of the equation.
-3x + 8xy + 3x2y + 3x + 4y = 0 + 3x

Reorder the terms:
-3x + 3x + 8xy + 3x2y + 4y = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + 8xy + 3x2y + 4y = 0 + 3x
8xy + 3x2y + 4y = 0 + 3x
Remove the zero:
8xy + 3x2y + 4y = 3x

Add '-8xy' to each side of the equation.
8xy + 3x2y + -8xy + 4y = 3x + -8xy

Reorder the terms:
8xy + -8xy + 3x2y + 4y = 3x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 3x2y + 4y = 3x + -8xy
3x2y + 4y = 3x + -8xy

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + 4y = 3x + -8xy + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 4y = 3x + -8xy + -3x2y
4y = 3x + -8xy + -3x2y

Add '-4y' to each side of the equation.
4y + -4y = 3x + -8xy + -3x2y + -4y

Combine like terms: 4y + -4y = 0
0 = 3x + -8xy + -3x2y + -4y

Simplifying
0 = 3x + -8xy + -3x2y + -4y

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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