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

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


Simplifying
(4x + -5y + 3) * dx + (2 + -5x + -1y) * dy = 0

Reorder the terms:
(3 + 4x + -5y) * dx + (2 + -5x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 4x + -5y) + (2 + -5x + -1y) * dy = 0
(3 * dx + 4x * dx + -5y * dx) + (2 + -5x + -1y) * dy = 0

Reorder the terms:
(3dx + -5dxy + 4dx2) + (2 + -5x + -1y) * dy = 0
(3dx + -5dxy + 4dx2) + (2 + -5x + -1y) * dy = 0

Reorder the terms for easier multiplication:
3dx + -5dxy + 4dx2 + dy(2 + -5x + -1y) = 0
3dx + -5dxy + 4dx2 + (2 * dy + -5x * dy + -1y * dy) = 0

Reorder the terms:
3dx + -5dxy + 4dx2 + (-5dxy + 2dy + -1dy2) = 0
3dx + -5dxy + 4dx2 + (-5dxy + 2dy + -1dy2) = 0

Reorder the terms:
3dx + -5dxy + -5dxy + 4dx2 + 2dy + -1dy2 = 0

Combine like terms: -5dxy + -5dxy = -10dxy
3dx + -10dxy + 4dx2 + 2dy + -1dy2 = 0

Solving
3dx + -10dxy + 4dx2 + 2dy + -1dy2 = 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 + 2y + -1y2) = 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 + 2y + -1y2)' equal to zero and attempt to solve:

Simplifying
3x + -10xy + 4x2 + 2y + -1y2 = 0

Solving
3x + -10xy + 4x2 + 2y + -1y2 = 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 + 2y + -3x + -1y2 = 0 + -3x

Reorder the terms:
3x + -3x + -10xy + 4x2 + 2y + -1y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + -10xy + 4x2 + 2y + -1y2 = 0 + -3x
-10xy + 4x2 + 2y + -1y2 = 0 + -3x
Remove the zero:
-10xy + 4x2 + 2y + -1y2 = -3x

Add '10xy' to each side of the equation.
-10xy + 4x2 + 2y + 10xy + -1y2 = -3x + 10xy

Reorder the terms:
-10xy + 10xy + 4x2 + 2y + -1y2 = -3x + 10xy

Combine like terms: -10xy + 10xy = 0
0 + 4x2 + 2y + -1y2 = -3x + 10xy
4x2 + 2y + -1y2 = -3x + 10xy

Add '-4x2' to each side of the equation.
4x2 + 2y + -4x2 + -1y2 = -3x + 10xy + -4x2

Reorder the terms:
4x2 + -4x2 + 2y + -1y2 = -3x + 10xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 2y + -1y2 = -3x + 10xy + -4x2
2y + -1y2 = -3x + 10xy + -4x2

Add '-2y' to each side of the equation.
2y + -2y + -1y2 = -3x + 10xy + -4x2 + -2y

Combine like terms: 2y + -2y = 0
0 + -1y2 = -3x + 10xy + -4x2 + -2y
-1y2 = -3x + 10xy + -4x2 + -2y

Add 'y2' to each side of the equation.
-1y2 + y2 = -3x + 10xy + -4x2 + -2y + y2

Combine like terms: -1y2 + y2 = 0
0 = -3x + 10xy + -4x2 + -2y + y2

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

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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