(3y+x)dx+(x+5y-8)dy=0

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Solution for (3y+x)dx+(x+5y-8)dy=0 equation: 


Simplifying
(3y + x) * dx + (x + 5y + -8) * dy = 0

Reorder the terms:
(x + 3y) * dx + (x + 5y + -8) * dy = 0

Reorder the terms for easier multiplication:
dx(x + 3y) + (x + 5y + -8) * dy = 0
(x * dx + 3y * dx) + (x + 5y + -8) * dy = 0

Reorder the terms:
(3dxy + dx2) + (x + 5y + -8) * dy = 0
(3dxy + dx2) + (x + 5y + -8) * dy = 0

Reorder the terms:
3dxy + dx2 + (-8 + x + 5y) * dy = 0

Reorder the terms for easier multiplication:
3dxy + dx2 + dy(-8 + x + 5y) = 0
3dxy + dx2 + (-8 * dy + x * dy + 5y * dy) = 0

Reorder the terms:
3dxy + dx2 + (dxy + -8dy + 5dy2) = 0
3dxy + dx2 + (dxy + -8dy + 5dy2) = 0

Reorder the terms:
3dxy + dxy + dx2 + -8dy + 5dy2 = 0

Combine like terms: 3dxy + dxy = 4dxy
4dxy + dx2 + -8dy + 5dy2 = 0

Solving
4dxy + dx2 + -8dy + 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(4xy + x2 + -8y + 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 '(4xy + x2 + -8y + 5y2)' equal to zero and attempt to solve:

Simplifying
4xy + x2 + -8y + 5y2 = 0

Solving
4xy + x2 + -8y + 5y2 = 0

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

Add '-4xy' to each side of the equation.
4xy + x2 + -8y + -4xy + 5y2 = 0 + -4xy

Reorder the terms:
4xy + -4xy + x2 + -8y + 5y2 = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + x2 + -8y + 5y2 = 0 + -4xy
x2 + -8y + 5y2 = 0 + -4xy
Remove the zero:
x2 + -8y + 5y2 = -4xy

Add '-1x2' to each side of the equation.
x2 + -8y + -1x2 + 5y2 = -4xy + -1x2

Reorder the terms:
x2 + -1x2 + -8y + 5y2 = -4xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -8y + 5y2 = -4xy + -1x2
-8y + 5y2 = -4xy + -1x2

Add '8y' to each side of the equation.
-8y + 8y + 5y2 = -4xy + -1x2 + 8y

Combine like terms: -8y + 8y = 0
0 + 5y2 = -4xy + -1x2 + 8y
5y2 = -4xy + -1x2 + 8y

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -4xy + -1x2 + 8y + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -4xy + -1x2 + 8y + -5y2

Simplifying
0 = -4xy + -1x2 + 8y + -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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