(3y+7x)dy=(1-2x)dx

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Solution for (3y+7x)dy=(1-2x)dx equation: 


Simplifying
(3y + 7x) * dy = (1 + -2x) * dx

Reorder the terms:
(7x + 3y) * dy = (1 + -2x) * dx

Reorder the terms for easier multiplication:
dy(7x + 3y) = (1 + -2x) * dx
(7x * dy + 3y * dy) = (1 + -2x) * dx
(7dxy + 3dy2) = (1 + -2x) * dx

Reorder the terms for easier multiplication:
7dxy + 3dy2 = dx(1 + -2x)
7dxy + 3dy2 = (1 * dx + -2x * dx)
7dxy + 3dy2 = (1dx + -2dx2)

Solving
7dxy + 3dy2 = 1dx + -2dx2

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
7dxy + -1dx + 3dy2 = 1dx + -1dx + -2dx2

Reorder the terms:
-1dx + 7dxy + 3dy2 = 1dx + -1dx + -2dx2

Combine like terms: 1dx + -1dx = 0
-1dx + 7dxy + 3dy2 = 0 + -2dx2
-1dx + 7dxy + 3dy2 = -2dx2

Add '2dx2' to each side of the equation.
-1dx + 7dxy + 2dx2 + 3dy2 = -2dx2 + 2dx2

Combine like terms: -2dx2 + 2dx2 = 0
-1dx + 7dxy + 2dx2 + 3dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + 7xy + 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 '(-1x + 7xy + 2x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
-1x + 7xy + 2x2 + 3y2 = 0

Solving
-1x + 7xy + 2x2 + 3y2 = 0

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

Add 'x' to each side of the equation.
-1x + 7xy + 2x2 + x + 3y2 = 0 + x

Reorder the terms:
-1x + x + 7xy + 2x2 + 3y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 7xy + 2x2 + 3y2 = 0 + x
7xy + 2x2 + 3y2 = 0 + x
Remove the zero:
7xy + 2x2 + 3y2 = x

Add '-7xy' to each side of the equation.
7xy + 2x2 + -7xy + 3y2 = x + -7xy

Reorder the terms:
7xy + -7xy + 2x2 + 3y2 = x + -7xy

Combine like terms: 7xy + -7xy = 0
0 + 2x2 + 3y2 = x + -7xy
2x2 + 3y2 = x + -7xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 3y2 = x + -7xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 3y2 = x + -7xy + -2x2
3y2 = x + -7xy + -2x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = x + -7xy + -2x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = x + -7xy + -2x2 + -3y2

Simplifying
0 = x + -7xy + -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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