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

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


Simplifying
(X + y) * dx + -1(3x + 8y) * dy = 0

Reorder the terms for easier multiplication:
dx(X + y) + -1(3x + 8y) * dy = 0
(X * dx + y * dx) + -1(3x + 8y) * dy = 0
(dxX + dxy) + -1(3x + 8y) * dy = 0

Reorder the terms for easier multiplication:
dxX + dxy + -1dy(3x + 8y) = 0
dxX + dxy + (3x * -1dy + 8y * -1dy) = 0
dxX + dxy + (-3dxy + -8dy2) = 0

Combine like terms: dxy + -3dxy = -2dxy
dxX + -2dxy + -8dy2 = 0

Solving
dxX + -2dxy + -8dy2 = 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(xX + -2xy + -8y2) = 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 '(xX + -2xy + -8y2)' equal to zero and attempt to solve:

Simplifying
xX + -2xy + -8y2 = 0

Solving
xX + -2xy + -8y2 = 0

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

Add '-1xX' to each side of the equation.
xX + -2xy + -1xX + -8y2 = 0 + -1xX

Reorder the terms:
xX + -1xX + -2xy + -8y2 = 0 + -1xX

Combine like terms: xX + -1xX = 0
0 + -2xy + -8y2 = 0 + -1xX
-2xy + -8y2 = 0 + -1xX
Remove the zero:
-2xy + -8y2 = -1xX

Add '2xy' to each side of the equation.
-2xy + 2xy + -8y2 = -1xX + 2xy

Combine like terms: -2xy + 2xy = 0
0 + -8y2 = -1xX + 2xy
-8y2 = -1xX + 2xy

Add '8y2' to each side of the equation.
-8y2 + 8y2 = -1xX + 2xy + 8y2

Combine like terms: -8y2 + 8y2 = 0
0 = -1xX + 2xy + 8y2

Simplifying
0 = -1xX + 2xy + 8y2

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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