(2x-1)dx+(7y+3)dy=0

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Solution for (2x-1)dx+(7y+3)dy=0 equation: 


Simplifying
(2x + -1) * dx + (7y + 3) * dy = 0

Reorder the terms:
(-1 + 2x) * dx + (7y + 3) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2x) + (7y + 3) * dy = 0
(-1 * dx + 2x * dx) + (7y + 3) * dy = 0
(-1dx + 2dx2) + (7y + 3) * dy = 0

Reorder the terms:
-1dx + 2dx2 + (3 + 7y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 2dx2 + dy(3 + 7y) = 0
-1dx + 2dx2 + (3 * dy + 7y * dy) = 0
-1dx + 2dx2 + (3dy + 7dy2) = 0

Solving
-1dx + 2dx2 + 3dy + 7dy2 = 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(-1x + 2x2 + 3y + 7y2) = 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 + 2x2 + 3y + 7y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = x + -2x2 + -3y + -7y2

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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