(4x+8y)dx-(8x+3y)dy=0

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Solution for (4x+8y)dx-(8x+3y)dy=0 equation: 


Simplifying
(4x + 8y) * dx + -1(8x + 3y) * dy = 0

Reorder the terms for easier multiplication:
dx(4x + 8y) + -1(8x + 3y) * dy = 0
(4x * dx + 8y * dx) + -1(8x + 3y) * dy = 0

Reorder the terms:
(8dxy + 4dx2) + -1(8x + 3y) * dy = 0
(8dxy + 4dx2) + -1(8x + 3y) * dy = 0

Reorder the terms for easier multiplication:
8dxy + 4dx2 + -1dy(8x + 3y) = 0
8dxy + 4dx2 + (8x * -1dy + 3y * -1dy) = 0
8dxy + 4dx2 + (-8dxy + -3dy2) = 0

Reorder the terms:
8dxy + -8dxy + 4dx2 + -3dy2 = 0

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

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

Simplifying
4x2 + -3y2 = 0

Solving
4x2 + -3y2 = 0

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

Add '-4x2' to each side of the equation.
4x2 + -4x2 + -3y2 = 0 + -4x2

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

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

Combine like terms: -3y2 + 3y2 = 0
0 = -4x2 + 3y2

Simplifying
0 = -4x2 + 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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