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

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


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

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

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

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

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

Solving
3dx + 2dx2 + -5dy + 4dy2 = 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 + 2x2 + -5y + 4y2) = 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 + 2x2 + -5y + 4y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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