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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -5x + 4xy + -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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