(3x+6)dx+(5y)dy=0

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Solution for (3x+6)dx+(5y)dy=0 equation: 


Simplifying
(3x + 6) * dx + (5y) * dy = 0

Reorder the terms:
(6 + 3x) * dx + (5y) * dy = 0

Reorder the terms for easier multiplication:
dx(6 + 3x) + (5y) * dy = 0
(6 * dx + 3x * dx) + (5y) * dy = 0
(6dx + 3dx2) + (5y) * dy = 0

Remove parenthesis around (5y)
6dx + 3dx2 + 5y * dy = 0

Multiply y * dy
6dx + 3dx2 + 5dy2 = 0

Solving
6dx + 3dx2 + 5dy2 = 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(6x + 3x2 + 5y2) = 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 '(6x + 3x2 + 5y2)' equal to zero and attempt to solve:

Simplifying
6x + 3x2 + 5y2 = 0

Solving
6x + 3x2 + 5y2 = 0

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

Add '-6x' to each side of the equation.
6x + 3x2 + -6x + 5y2 = 0 + -6x

Reorder the terms:
6x + -6x + 3x2 + 5y2 = 0 + -6x

Combine like terms: 6x + -6x = 0
0 + 3x2 + 5y2 = 0 + -6x
3x2 + 5y2 = 0 + -6x
Remove the zero:
3x2 + 5y2 = -6x

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 5y2 = -6x + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 5y2 = -6x + -3x2
5y2 = -6x + -3x2

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -6x + -3x2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -6x + -3x2 + -5y2

Simplifying
0 = -6x + -3x2 + -5y2

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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