(16xy-3x^2)dx+(8x^2+2y)dy=0

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Solution for (16xy-3x^2)dx+(8x^2+2y)dy=0 equation: 


Simplifying
(16xy + -3x2) * dx + (8x2 + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx(16xy + -3x2) + (8x2 + 2y) * dy = 0
(16xy * dx + -3x2 * dx) + (8x2 + 2y) * dy = 0
(16dx2y + -3dx3) + (8x2 + 2y) * dy = 0

Reorder the terms for easier multiplication:
16dx2y + -3dx3 + dy(8x2 + 2y) = 0
16dx2y + -3dx3 + (8x2 * dy + 2y * dy) = 0
16dx2y + -3dx3 + (8dx2y + 2dy2) = 0

Reorder the terms:
16dx2y + 8dx2y + -3dx3 + 2dy2 = 0

Combine like terms: 16dx2y + 8dx2y = 24dx2y
24dx2y + -3dx3 + 2dy2 = 0

Solving
24dx2y + -3dx3 + 2dy2 = 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(24x2y + -3x3 + 2y2) = 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 '(24x2y + -3x3 + 2y2)' equal to zero and attempt to solve:

Simplifying
24x2y + -3x3 + 2y2 = 0

Solving
24x2y + -3x3 + 2y2 = 0

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

Add '-24x2y' to each side of the equation.
24x2y + -3x3 + -24x2y + 2y2 = 0 + -24x2y

Reorder the terms:
24x2y + -24x2y + -3x3 + 2y2 = 0 + -24x2y

Combine like terms: 24x2y + -24x2y = 0
0 + -3x3 + 2y2 = 0 + -24x2y
-3x3 + 2y2 = 0 + -24x2y
Remove the zero:
-3x3 + 2y2 = -24x2y

Add '3x3' to each side of the equation.
-3x3 + 3x3 + 2y2 = -24x2y + 3x3

Combine like terms: -3x3 + 3x3 = 0
0 + 2y2 = -24x2y + 3x3
2y2 = -24x2y + 3x3

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -24x2y + 3x3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -24x2y + 3x3 + -2y2

Simplifying
0 = -24x2y + 3x3 + -2y2

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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