2dx+(2x+3y)dy=0

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Solution for 2dx+(2x+3y)dy=0 equation: 


Simplifying
2dx + (2x + 3y) * dy = 0

Reorder the terms for easier multiplication:
2dx + dy(2x + 3y) = 0
2dx + (2x * dy + 3y * dy) = 0
2dx + (2dxy + 3dy2) = 0

Solving
2dx + 2dxy + 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(2x + 2xy + 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 '(2x + 2xy + 3y2)' equal to zero and attempt to solve:

Simplifying
2x + 2xy + 3y2 = 0

Solving
2x + 2xy + 3y2 = 0

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

Add '-2x' to each side of the equation.
2x + 2xy + -2x + 3y2 = 0 + -2x

Reorder the terms:
2x + -2x + 2xy + 3y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 2xy + 3y2 = 0 + -2x
2xy + 3y2 = 0 + -2x
Remove the zero:
2xy + 3y2 = -2x

Add '-2xy' to each side of the equation.
2xy + -2xy + 3y2 = -2x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 3y2 = -2x + -2xy
3y2 = -2x + -2xy

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -2x + -2xy + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -2x + -2xy + -3y2

Simplifying
0 = -2x + -2xy + -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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