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

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


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

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

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

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

Reorder the terms for easier multiplication:
3dx + 5dxy + 4dx2 + dy(5x + -2y) = 0
3dx + 5dxy + 4dx2 + (5x * dy + -2y * dy) = 0
3dx + 5dxy + 4dx2 + (5dxy + -2dy2) = 0

Reorder the terms:
3dx + 5dxy + 5dxy + 4dx2 + -2dy2 = 0

Combine like terms: 5dxy + 5dxy = 10dxy
3dx + 10dxy + 4dx2 + -2dy2 = 0

Solving
3dx + 10dxy + 4dx2 + -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 + 10xy + 4x2 + -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 + 10xy + 4x2 + -2y2)' equal to zero and attempt to solve:

Simplifying
3x + 10xy + 4x2 + -2y2 = 0

Solving
3x + 10xy + 4x2 + -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 + 10xy + 4x2 + -3x + -2y2 = 0 + -3x

Reorder the terms:
3x + -3x + 10xy + 4x2 + -2y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 10xy + 4x2 + -2y2 = 0 + -3x
10xy + 4x2 + -2y2 = 0 + -3x
Remove the zero:
10xy + 4x2 + -2y2 = -3x

Add '-10xy' to each side of the equation.
10xy + 4x2 + -10xy + -2y2 = -3x + -10xy

Reorder the terms:
10xy + -10xy + 4x2 + -2y2 = -3x + -10xy

Combine like terms: 10xy + -10xy = 0
0 + 4x2 + -2y2 = -3x + -10xy
4x2 + -2y2 = -3x + -10xy

Add '-4x2' to each side of the equation.
4x2 + -4x2 + -2y2 = -3x + -10xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + -2y2 = -3x + -10xy + -4x2
-2y2 = -3x + -10xy + -4x2

Add '2y2' to each side of the equation.
-2y2 + 2y2 = -3x + -10xy + -4x2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = -3x + -10xy + -4x2 + 2y2

Simplifying
0 = -3x + -10xy + -4x2 + 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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