(2x-5y-2)dx+(5x-y-5)dy=0

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Solution for (2x-5y-2)dx+(5x-y-5)dy=0 equation: 


Simplifying
(2x + -5y + -2) * dx + (5x + -1y + -5) * dy = 0

Reorder the terms:
(-2 + 2x + -5y) * dx + (5x + -1y + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(-2 + 2x + -5y) + (5x + -1y + -5) * dy = 0
(-2 * dx + 2x * dx + -5y * dx) + (5x + -1y + -5) * dy = 0

Reorder the terms:
(-2dx + -5dxy + 2dx2) + (5x + -1y + -5) * dy = 0
(-2dx + -5dxy + 2dx2) + (5x + -1y + -5) * dy = 0

Reorder the terms:
-2dx + -5dxy + 2dx2 + (-5 + 5x + -1y) * dy = 0

Reorder the terms for easier multiplication:
-2dx + -5dxy + 2dx2 + dy(-5 + 5x + -1y) = 0
-2dx + -5dxy + 2dx2 + (-5 * dy + 5x * dy + -1y * dy) = 0

Reorder the terms:
-2dx + -5dxy + 2dx2 + (5dxy + -5dy + -1dy2) = 0
-2dx + -5dxy + 2dx2 + (5dxy + -5dy + -1dy2) = 0

Reorder the terms:
-2dx + -5dxy + 5dxy + 2dx2 + -5dy + -1dy2 = 0

Combine like terms: -5dxy + 5dxy = 0
-2dx + 0 + 2dx2 + -5dy + -1dy2 = 0
-2dx + 2dx2 + -5dy + -1dy2 = 0

Solving
-2dx + 2dx2 + -5dy + -1dy2 = 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 + 2x2 + -5y + -1y2) = 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 + 2x2 + -5y + -1y2)' equal to zero and attempt to solve:

Simplifying
-2x + 2x2 + -5y + -1y2 = 0

Solving
-2x + 2x2 + -5y + -1y2 = 0

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

Add '2x' to each side of the equation.
-2x + 2x2 + -5y + 2x + -1y2 = 0 + 2x

Reorder the terms:
-2x + 2x + 2x2 + -5y + -1y2 = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + 2x2 + -5y + -1y2 = 0 + 2x
2x2 + -5y + -1y2 = 0 + 2x
Remove the zero:
2x2 + -5y + -1y2 = 2x

Add '-2x2' to each side of the equation.
2x2 + -5y + -2x2 + -1y2 = 2x + -2x2

Reorder the terms:
2x2 + -2x2 + -5y + -1y2 = 2x + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -5y + -1y2 = 2x + -2x2
-5y + -1y2 = 2x + -2x2

Add '5y' to each side of the equation.
-5y + 5y + -1y2 = 2x + -2x2 + 5y

Combine like terms: -5y + 5y = 0
0 + -1y2 = 2x + -2x2 + 5y
-1y2 = 2x + -2x2 + 5y

Add 'y2' to each side of the equation.
-1y2 + y2 = 2x + -2x2 + 5y + y2

Combine like terms: -1y2 + y2 = 0
0 = 2x + -2x2 + 5y + y2

Simplifying
0 = 2x + -2x2 + 5y + y2

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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