(2x+5y)dx=(5x+3y)dy

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Solution for (2x+5y)dx=(5x+3y)dy equation: 


Simplifying
(2x + 5y) * dx = (5x + 3y) * dy

Reorder the terms for easier multiplication:
dx(2x + 5y) = (5x + 3y) * dy
(2x * dx + 5y * dx) = (5x + 3y) * dy

Reorder the terms:
(5dxy + 2dx2) = (5x + 3y) * dy
(5dxy + 2dx2) = (5x + 3y) * dy

Reorder the terms for easier multiplication:
5dxy + 2dx2 = dy(5x + 3y)
5dxy + 2dx2 = (5x * dy + 3y * dy)
5dxy + 2dx2 = (5dxy + 3dy2)

Add '-5dxy' to each side of the equation.
5dxy + -5dxy + 2dx2 = 5dxy + -5dxy + 3dy2

Combine like terms: 5dxy + -5dxy = 0
0 + 2dx2 = 5dxy + -5dxy + 3dy2
2dx2 = 5dxy + -5dxy + 3dy2

Combine like terms: 5dxy + -5dxy = 0
2dx2 = 0 + 3dy2
2dx2 = 3dy2

Solving
2dx2 = 3dy2

Solving for variable 'd'.

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

Add '-3dy2' to each side of the equation.
2dx2 + -3dy2 = 3dy2 + -3dy2

Combine like terms: 3dy2 + -3dy2 = 0
2dx2 + -3dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(2x2 + -3y2) = 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 '(2x2 + -3y2)' equal to zero and attempt to solve:

Simplifying
2x2 + -3y2 = 0

Solving
2x2 + -3y2 = 0

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

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

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

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

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

Simplifying
0 = -2x2 + 3y2

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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