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

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


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

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

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

Reorder the terms for easier multiplication:
8dxy + 3dx2 + dy(8x + 3y) = 0
8dxy + 3dx2 + (8x * dy + 3y * dy) = 0
8dxy + 3dx2 + (8dxy + 3dy2) = 0

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

Combine like terms: 8dxy + 8dxy = 16dxy
16dxy + 3dx2 + 3dy2 = 0

Solving
16dxy + 3dx2 + 3dy2 = 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(16xy + 3x2 + 3y2) = 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 '(16xy + 3x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
16xy + 3x2 + 3y2 = 0

Solving
16xy + 3x2 + 3y2 = 0

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

Add '-16xy' to each side of the equation.
16xy + 3x2 + -16xy + 3y2 = 0 + -16xy

Reorder the terms:
16xy + -16xy + 3x2 + 3y2 = 0 + -16xy

Combine like terms: 16xy + -16xy = 0
0 + 3x2 + 3y2 = 0 + -16xy
3x2 + 3y2 = 0 + -16xy
Remove the zero:
3x2 + 3y2 = -16xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 3y2 = -16xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 3y2 = -16xy + -3x2
3y2 = -16xy + -3x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -16xy + -3x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -16xy + -3x2 + -3y2

Simplifying
0 = -16xy + -3x2 + -3y2

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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