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

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


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

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

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

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

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

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

Reorder the terms:
2dx + -1dxy + 4dx2 + (dxy + 3dy + dy2) = 0
2dx + -1dxy + 4dx2 + (dxy + 3dy + dy2) = 0

Reorder the terms:
2dx + -1dxy + dxy + 4dx2 + 3dy + dy2 = 0

Combine like terms: -1dxy + dxy = 0
2dx + 0 + 4dx2 + 3dy + dy2 = 0
2dx + 4dx2 + 3dy + dy2 = 0

Solving
2dx + 4dx2 + 3dy + dy2 = 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 + 4x2 + 3y + y2) = 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 + 4x2 + 3y + y2)' equal to zero and attempt to solve:

Simplifying
2x + 4x2 + 3y + y2 = 0

Solving
2x + 4x2 + 3y + y2 = 0

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

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

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

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

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

Reorder the terms:
4x2 + -4x2 + 3y + y2 = -2x + -4x2

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

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

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

Add '-1y2' to each side of the equation.
y2 + -1y2 = -2x + -4x2 + -3y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -2x + -4x2 + -3y + -1y2

Simplifying
0 = -2x + -4x2 + -3y + -1y2

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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