(2x+3y)dx=(5y-7x)dy

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Solution for (2x+3y)dx=(5y-7x)dy equation: 


Simplifying
(2x + 3y) * dx = (5y + -7x) * dy

Reorder the terms for easier multiplication:
dx(2x + 3y) = (5y + -7x) * dy
(2x * dx + 3y * dx) = (5y + -7x) * dy

Reorder the terms:
(3dxy + 2dx2) = (5y + -7x) * dy
(3dxy + 2dx2) = (5y + -7x) * dy

Reorder the terms:
3dxy + 2dx2 = (-7x + 5y) * dy

Reorder the terms for easier multiplication:
3dxy + 2dx2 = dy(-7x + 5y)
3dxy + 2dx2 = (-7x * dy + 5y * dy)
3dxy + 2dx2 = (-7dxy + 5dy2)

Solving
3dxy + 2dx2 = -7dxy + 5dy2

Solving for variable 'd'.

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

Add '7dxy' to each side of the equation.
3dxy + 7dxy + 2dx2 = -7dxy + 7dxy + 5dy2

Combine like terms: 3dxy + 7dxy = 10dxy
10dxy + 2dx2 = -7dxy + 7dxy + 5dy2

Combine like terms: -7dxy + 7dxy = 0
10dxy + 2dx2 = 0 + 5dy2
10dxy + 2dx2 = 5dy2

Add '-5dy2' to each side of the equation.
10dxy + 2dx2 + -5dy2 = 5dy2 + -5dy2

Combine like terms: 5dy2 + -5dy2 = 0
10dxy + 2dx2 + -5dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(10xy + 2x2 + -5y2) = 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 '(10xy + 2x2 + -5y2)' equal to zero and attempt to solve:

Simplifying
10xy + 2x2 + -5y2 = 0

Solving
10xy + 2x2 + -5y2 = 0

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

Add '-10xy' to each side of the equation.
10xy + 2x2 + -10xy + -5y2 = 0 + -10xy

Reorder the terms:
10xy + -10xy + 2x2 + -5y2 = 0 + -10xy

Combine like terms: 10xy + -10xy = 0
0 + 2x2 + -5y2 = 0 + -10xy
2x2 + -5y2 = 0 + -10xy
Remove the zero:
2x2 + -5y2 = -10xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + -5y2 = -10xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -5y2 = -10xy + -2x2
-5y2 = -10xy + -2x2

Add '5y2' to each side of the equation.
-5y2 + 5y2 = -10xy + -2x2 + 5y2

Combine like terms: -5y2 + 5y2 = 0
0 = -10xy + -2x2 + 5y2

Simplifying
0 = -10xy + -2x2 + 5y2

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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