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

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


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

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

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

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

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

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

Combine like terms: 3dxy + 3dxy = 6dxy
-2dx + 6dxy + 4dx2 + -5dy2 = 0

Solving
-2dx + 6dxy + 4dx2 + -5dy2 = 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(-2x + 6xy + 4x2 + -5y2) = 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 '(-2x + 6xy + 4x2 + -5y2)' equal to zero and attempt to solve:

Simplifying
-2x + 6xy + 4x2 + -5y2 = 0

Solving
-2x + 6xy + 4x2 + -5y2 = 0

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

Add '2x' to each side of the equation.
-2x + 6xy + 4x2 + 2x + -5y2 = 0 + 2x

Reorder the terms:
-2x + 2x + 6xy + 4x2 + -5y2 = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + 6xy + 4x2 + -5y2 = 0 + 2x
6xy + 4x2 + -5y2 = 0 + 2x
Remove the zero:
6xy + 4x2 + -5y2 = 2x

Add '-6xy' to each side of the equation.
6xy + 4x2 + -6xy + -5y2 = 2x + -6xy

Reorder the terms:
6xy + -6xy + 4x2 + -5y2 = 2x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + 4x2 + -5y2 = 2x + -6xy
4x2 + -5y2 = 2x + -6xy

Add '-4x2' to each side of the equation.
4x2 + -4x2 + -5y2 = 2x + -6xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + -5y2 = 2x + -6xy + -4x2
-5y2 = 2x + -6xy + -4x2

Add '5y2' to each side of the equation.
-5y2 + 5y2 = 2x + -6xy + -4x2 + 5y2

Combine like terms: -5y2 + 5y2 = 0
0 = 2x + -6xy + -4x2 + 5y2

Simplifying
0 = 2x + -6xy + -4x2 + 5y2

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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