-(x+2y)dx+(2x+y)dy=0

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


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

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

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

Reorder the terms for easier multiplication:
-2dxy + -1dx2 + dy(2x + y) = 0
-2dxy + -1dx2 + (2x * dy + y * dy) = 0
-2dxy + -1dx2 + (2dxy + dy2) = 0

Reorder the terms:
-2dxy + 2dxy + -1dx2 + dy2 = 0

Combine like terms: -2dxy + 2dxy = 0
0 + -1dx2 + dy2 = 0
-1dx2 + dy2 = 0

Solving
-1dx2 + 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(-1x2 + y2) = 0

Factor a difference between two squares.
d((x + y)(-1x + y)) = 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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

Combine like terms: x + -1x = 0
0 + y = 0 + -1x
y = 0 + -1x
Remove the zero:
y = -1x

Add '-1y' to each side of the equation.
y + -1y = -1x + -1y

Combine like terms: y + -1y = 0
0 = -1x + -1y

Simplifying
0 = -1x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

Combine like terms: -1x + x = 0
0 + y = 0 + x
y = 0 + x
Remove the zero:
y = x

Add '-1y' to each side of the equation.
y + -1y = x + -1y

Combine like terms: y + -1y = 0
0 = x + -1y

Simplifying
0 = x + -1y

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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