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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
x2 + 5y + -1x2 + -4y2 = -3x + -1x2

Reorder the terms:
x2 + -1x2 + 5y + -4y2 = -3x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 5y + -4y2 = -3x + -1x2
5y + -4y2 = -3x + -1x2

Add '-5y' to each side of the equation.
5y + -5y + -4y2 = -3x + -1x2 + -5y

Combine like terms: 5y + -5y = 0
0 + -4y2 = -3x + -1x2 + -5y
-4y2 = -3x + -1x2 + -5y

Add '4y2' to each side of the equation.
-4y2 + 4y2 = -3x + -1x2 + -5y + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = -3x + -1x2 + -5y + 4y2

Simplifying
0 = -3x + -1x2 + -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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