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

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


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

Reorder the terms:
(1 + 2x) * dx + (4y + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 2x) + (4y + 2) * dy = 0
(1 * dx + 2x * dx) + (4y + 2) * dy = 0
(1dx + 2dx2) + (4y + 2) * dy = 0

Reorder the terms:
1dx + 2dx2 + (2 + 4y) * dy = 0

Reorder the terms for easier multiplication:
1dx + 2dx2 + dy(2 + 4y) = 0
1dx + 2dx2 + (2 * dy + 4y * dy) = 0
1dx + 2dx2 + (2dy + 4dy2) = 0

Solving
1dx + 2dx2 + 2dy + 4dy2 = 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(x + 2x2 + 2y + 4y2) = 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 '(x + 2x2 + 2y + 4y2)' equal to zero and attempt to solve:

Simplifying
x + 2x2 + 2y + 4y2 = 0

Solving
x + 2x2 + 2y + 4y2 = 0

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

Add '-1x' to each side of the equation.
x + 2x2 + 2y + -1x + 4y2 = 0 + -1x

Reorder the terms:
x + -1x + 2x2 + 2y + 4y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 2x2 + 2y + 4y2 = 0 + -1x
2x2 + 2y + 4y2 = 0 + -1x
Remove the zero:
2x2 + 2y + 4y2 = -1x

Add '-2x2' to each side of the equation.
2x2 + 2y + -2x2 + 4y2 = -1x + -2x2

Reorder the terms:
2x2 + -2x2 + 2y + 4y2 = -1x + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2y + 4y2 = -1x + -2x2
2y + 4y2 = -1x + -2x2

Add '-2y' to each side of the equation.
2y + -2y + 4y2 = -1x + -2x2 + -2y

Combine like terms: 2y + -2y = 0
0 + 4y2 = -1x + -2x2 + -2y
4y2 = -1x + -2x2 + -2y

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -1x + -2x2 + -2y + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -1x + -2x2 + -2y + -4y2

Simplifying
0 = -1x + -2x2 + -2y + -4y2

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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