(2x+3y)dx-4(x+1)dy=0

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Solution for (2x+3y)dx-4(x+1)dy=0 equation: 


Simplifying
(2x + 3y) * dx + -4(x + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + 3y) + -4(x + 1) * dy = 0
(2x * dx + 3y * dx) + -4(x + 1) * dy = 0

Reorder the terms:
(3dxy + 2dx2) + -4(x + 1) * dy = 0
(3dxy + 2dx2) + -4(x + 1) * dy = 0

Reorder the terms:
3dxy + 2dx2 + -4(1 + x) * dy = 0

Reorder the terms for easier multiplication:
3dxy + 2dx2 + -4dy(1 + x) = 0
3dxy + 2dx2 + (1 * -4dy + x * -4dy) = 0

Reorder the terms:
3dxy + 2dx2 + (-4dxy + -4dy) = 0
3dxy + 2dx2 + (-4dxy + -4dy) = 0

Reorder the terms:
3dxy + -4dxy + 2dx2 + -4dy = 0

Combine like terms: 3dxy + -4dxy = -1dxy
-1dxy + 2dx2 + -4dy = 0

Solving
-1dxy + 2dx2 + -4dy = 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(-1xy + 2x2 + -4y) = 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 '(-1xy + 2x2 + -4y)' equal to zero and attempt to solve:

Simplifying
-1xy + 2x2 + -4y = 0

Solving
-1xy + 2x2 + -4y = 0

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

Add 'xy' to each side of the equation.
-1xy + 2x2 + xy + -4y = 0 + xy

Reorder the terms:
-1xy + xy + 2x2 + -4y = 0 + xy

Combine like terms: -1xy + xy = 0
0 + 2x2 + -4y = 0 + xy
2x2 + -4y = 0 + xy
Remove the zero:
2x2 + -4y = xy

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

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

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

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

Simplifying
0 = xy + -2x2 + 4y

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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