(3x+8xy^2)dx+(2y+6x^2y)dy=0

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Solution for (3x+8xy^2)dx+(2y+6x^2y)dy=0 equation: 


Simplifying
(3x + 8xy2) * dx + (2y + 6x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(3x + 8xy2) + (2y + 6x2y) * dy = 0
(3x * dx + 8xy2 * dx) + (2y + 6x2y) * dy = 0
(3dx2 + 8dx2y2) + (2y + 6x2y) * dy = 0

Reorder the terms:
3dx2 + 8dx2y2 + (6x2y + 2y) * dy = 0

Reorder the terms for easier multiplication:
3dx2 + 8dx2y2 + dy(6x2y + 2y) = 0
3dx2 + 8dx2y2 + (6x2y * dy + 2y * dy) = 0
3dx2 + 8dx2y2 + (6dx2y2 + 2dy2) = 0

Combine like terms: 8dx2y2 + 6dx2y2 = 14dx2y2
3dx2 + 14dx2y2 + 2dy2 = 0

Solving
3dx2 + 14dx2y2 + 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(3x2 + 14x2y2 + 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 '(3x2 + 14x2y2 + 2y2)' equal to zero and attempt to solve:

Simplifying
3x2 + 14x2y2 + 2y2 = 0

Solving
3x2 + 14x2y2 + 2y2 = 0

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

Add '-3x2' to each side of the equation.
3x2 + 14x2y2 + -3x2 + 2y2 = 0 + -3x2

Reorder the terms:
3x2 + -3x2 + 14x2y2 + 2y2 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 14x2y2 + 2y2 = 0 + -3x2
14x2y2 + 2y2 = 0 + -3x2
Remove the zero:
14x2y2 + 2y2 = -3x2

Add '-14x2y2' to each side of the equation.
14x2y2 + -14x2y2 + 2y2 = -3x2 + -14x2y2

Combine like terms: 14x2y2 + -14x2y2 = 0
0 + 2y2 = -3x2 + -14x2y2
2y2 = -3x2 + -14x2y2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -3x2 + -14x2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -3x2 + -14x2y2 + -2y2

Simplifying
0 = -3x2 + -14x2y2 + -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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