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

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


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

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

Reorder the terms for easier multiplication:
2dxy + -2dy2 = dx(2x + 7y)
2dxy + -2dy2 = (2x * dx + 7y * dx)

Reorder the terms:
2dxy + -2dy2 = (7dxy + 2dx2)
2dxy + -2dy2 = (7dxy + 2dx2)

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

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.
2dxy + -7dxy + -2dy2 = 7dxy + -7dxy + 2dx2

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1d'.
-1d(5xy + 2x2 + 2y2) = 0

Factor a trinomial.
-1d((2x + y)(x + 2y)) = 0

Ignore the factor -1.

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 + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

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

Simplifying
0 = -2x + -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 '(x + 2y)' equal to zero and attempt to solve:

Simplifying
x + 2y = 0

Solving
x + 2y = 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 + 2y = 0 + -1x

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

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

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

Simplifying
0 = -1x + -2y

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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