2x*dx+(xy+5x)*dy=0

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Solution for 2x*dx+(xy+5x)*dy=0 equation: 


Simplifying
2x * dx + (xy + 5x) * dy = 0

Multiply x * dx
2dx2 + (xy + 5x) * dy = 0

Reorder the terms:
2dx2 + (5x + xy) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + dy(5x + xy) = 0
2dx2 + (5x * dy + xy * dy) = 0
2dx2 + (5dxy + dxy2) = 0

Reorder the terms:
5dxy + dxy2 + 2dx2 = 0

Solving
5dxy + dxy2 + 2dx2 = 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), 'dx'.
dx(5y + y2 + 2x) = 0


Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(5y + y2 + 2x)' equal to zero and attempt to solve:

Simplifying
5y + y2 + 2x = 0

Reorder the terms:
2x + 5y + y2 = 0

Solving
2x + 5y + 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 + 5y + -2x + y2 = 0 + -2x

Reorder the terms:
2x + -2x + 5y + y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 5y + y2 = 0 + -2x
5y + y2 = 0 + -2x
Remove the zero:
5y + y2 = -2x

Add '-5y' to each side of the equation.
5y + -5y + y2 = -2x + -5y

Combine like terms: 5y + -5y = 0
0 + y2 = -2x + -5y
y2 = -2x + -5y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -2x + -5y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -2x + -5y + -1y2

Simplifying
0 = -2x + -5y + -1y2

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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