(2x+y)dx=-(2x^2y+4)dy

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Solution for (2x+y)dx=-(2x^2y+4)dy equation: 


Simplifying
(2x + y) * dx = -1(2x2y + 4) * dy

Reorder the terms for easier multiplication:
dx(2x + y) = -1(2x2y + 4) * dy
(2x * dx + y * dx) = -1(2x2y + 4) * dy

Reorder the terms:
(dxy + 2dx2) = -1(2x2y + 4) * dy
(dxy + 2dx2) = -1(2x2y + 4) * dy

Reorder the terms:
dxy + 2dx2 = -1(4 + 2x2y) * dy

Reorder the terms for easier multiplication:
dxy + 2dx2 = -1dy(4 + 2x2y)
dxy + 2dx2 = (4 * -1dy + 2x2y * -1dy)

Reorder the terms:
dxy + 2dx2 = (-2dx2y2 + -4dy)
dxy + 2dx2 = (-2dx2y2 + -4dy)

Solving
dxy + 2dx2 = -2dx2y2 + -4dy

Solving for variable 'd'.

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

Add '2dx2y2' to each side of the equation.
dxy + 2dx2 + 2dx2y2 = -2dx2y2 + 2dx2y2 + -4dy

Combine like terms: -2dx2y2 + 2dx2y2 = 0
dxy + 2dx2 + 2dx2y2 = 0 + -4dy
dxy + 2dx2 + 2dx2y2 = -4dy

Add '4dy' to each side of the equation.
dxy + 2dx2 + 2dx2y2 + 4dy = -4dy + 4dy

Combine like terms: -4dy + 4dy = 0
dxy + 2dx2 + 2dx2y2 + 4dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(xy + 2x2 + 2x2y2 + 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 '(xy + 2x2 + 2x2y2 + 4y)' equal to zero and attempt to solve:

Simplifying
xy + 2x2 + 2x2y2 + 4y = 0

Solving
xy + 2x2 + 2x2y2 + 4y = 0

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

Add '-1xy' to each side of the equation.
xy + 2x2 + 2x2y2 + -1xy + 4y = 0 + -1xy

Reorder the terms:
xy + -1xy + 2x2 + 2x2y2 + 4y = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + 2x2 + 2x2y2 + 4y = 0 + -1xy
2x2 + 2x2y2 + 4y = 0 + -1xy
Remove the zero:
2x2 + 2x2y2 + 4y = -1xy

Add '-2x2' to each side of the equation.
2x2 + 2x2y2 + -2x2 + 4y = -1xy + -2x2

Reorder the terms:
2x2 + -2x2 + 2x2y2 + 4y = -1xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2x2y2 + 4y = -1xy + -2x2
2x2y2 + 4y = -1xy + -2x2

Add '-2x2y2' to each side of the equation.
2x2y2 + -2x2y2 + 4y = -1xy + -2x2 + -2x2y2

Combine like terms: 2x2y2 + -2x2y2 = 0
0 + 4y = -1xy + -2x2 + -2x2y2
4y = -1xy + -2x2 + -2x2y2

Add '-4y' to each side of the equation.
4y + -4y = -1xy + -2x2 + -2x2y2 + -4y

Combine like terms: 4y + -4y = 0
0 = -1xy + -2x2 + -2x2y2 + -4y

Simplifying
0 = -1xy + -2x2 + -2x2y2 + -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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