(2xy+4x+3)dx+(x^2+2y-5)dy=0

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Solution for (2xy+4x+3)dx+(x^2+2y-5)dy=0 equation: 


Simplifying
(2xy + 4x + 3) * dx + (x2 + 2y + -5) * dy = 0

Reorder the terms:
(3 + 4x + 2xy) * dx + (x2 + 2y + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 4x + 2xy) + (x2 + 2y + -5) * dy = 0
(3 * dx + 4x * dx + 2xy * dx) + (x2 + 2y + -5) * dy = 0
(3dx + 4dx2 + 2dx2y) + (x2 + 2y + -5) * dy = 0

Reorder the terms:
3dx + 4dx2 + 2dx2y + (-5 + x2 + 2y) * dy = 0

Reorder the terms for easier multiplication:
3dx + 4dx2 + 2dx2y + dy(-5 + x2 + 2y) = 0
3dx + 4dx2 + 2dx2y + (-5 * dy + x2 * dy + 2y * dy) = 0

Reorder the terms:
3dx + 4dx2 + 2dx2y + (dx2y + -5dy + 2dy2) = 0
3dx + 4dx2 + 2dx2y + (dx2y + -5dy + 2dy2) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
3dx + 4dx2 + 3dx2y + -5dy + 2dy2 = 0

Solving
3dx + 4dx2 + 3dx2y + -5dy + 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(3x + 4x2 + 3x2y + -5y + 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 '(3x + 4x2 + 3x2y + -5y + 2y2)' equal to zero and attempt to solve:

Simplifying
3x + 4x2 + 3x2y + -5y + 2y2 = 0

Solving
3x + 4x2 + 3x2y + -5y + 2y2 = 0

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

Add '-3x' to each side of the equation.
3x + 4x2 + 3x2y + -5y + -3x + 2y2 = 0 + -3x

Reorder the terms:
3x + -3x + 4x2 + 3x2y + -5y + 2y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 4x2 + 3x2y + -5y + 2y2 = 0 + -3x
4x2 + 3x2y + -5y + 2y2 = 0 + -3x
Remove the zero:
4x2 + 3x2y + -5y + 2y2 = -3x

Add '-4x2' to each side of the equation.
4x2 + 3x2y + -5y + -4x2 + 2y2 = -3x + -4x2

Reorder the terms:
4x2 + -4x2 + 3x2y + -5y + 2y2 = -3x + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 3x2y + -5y + 2y2 = -3x + -4x2
3x2y + -5y + 2y2 = -3x + -4x2

Add '-3x2y' to each side of the equation.
3x2y + -5y + -3x2y + 2y2 = -3x + -4x2 + -3x2y

Reorder the terms:
3x2y + -3x2y + -5y + 2y2 = -3x + -4x2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + -5y + 2y2 = -3x + -4x2 + -3x2y
-5y + 2y2 = -3x + -4x2 + -3x2y

Add '5y' to each side of the equation.
-5y + 5y + 2y2 = -3x + -4x2 + -3x2y + 5y

Combine like terms: -5y + 5y = 0
0 + 2y2 = -3x + -4x2 + -3x2y + 5y
2y2 = -3x + -4x2 + -3x2y + 5y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -3x + -4x2 + -3x2y + 5y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -3x + -4x2 + -3x2y + 5y + -2y2

Simplifying
0 = -3x + -4x2 + -3x2y + 5y + -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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