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

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


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

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

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

Reorder the terms:
2dxy + 3dy2 = (-2dxy + 2dx2)
2dxy + 3dy2 = (-2dxy + 2dx2)

Solving
2dxy + 3dy2 = -2dxy + 2dx2

Solving for variable 'd'.

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

Add '2dxy' to each side of the equation.
2dxy + 2dxy + 3dy2 = -2dxy + 2dxy + 2dx2

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + 3dy2 = -2dxy + 2dxy + 2dx2

Combine like terms: -2dxy + 2dxy = 0
4dxy + 3dy2 = 0 + 2dx2
4dxy + 3dy2 = 2dx2

Add '-2dx2' to each side of the equation.
4dxy + -2dx2 + 3dy2 = 2dx2 + -2dx2

Combine like terms: 2dx2 + -2dx2 = 0
4dxy + -2dx2 + 3dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(4xy + -2x2 + 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 '(4xy + -2x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
4xy + -2x2 + 3y2 = 0

Solving
4xy + -2x2 + 3y2 = 0

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

Add '-4xy' to each side of the equation.
4xy + -2x2 + -4xy + 3y2 = 0 + -4xy

Reorder the terms:
4xy + -4xy + -2x2 + 3y2 = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + -2x2 + 3y2 = 0 + -4xy
-2x2 + 3y2 = 0 + -4xy
Remove the zero:
-2x2 + 3y2 = -4xy

Add '2x2' to each side of the equation.
-2x2 + 2x2 + 3y2 = -4xy + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + 3y2 = -4xy + 2x2
3y2 = -4xy + 2x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -4xy + 2x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -4xy + 2x2 + -3y2

Simplifying
0 = -4xy + 2x2 + -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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