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

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


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

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

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

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

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

Solving
-1dx + 2dx2 + 7dy + 3dy2 = 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 + 7y + 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 + 2x2 + 7y + 3y2)' equal to zero and attempt to solve: Simplifying -1x + 2x2 + 7y + 3y2 = 0 Solving -1x + 2x2 + 7y + 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 + 2x2 + 7y + x + 3y2 = 0 + x Reorder the terms: -1x + x + 2x2 + 7y + 3y2 = 0 + x Combine like terms: -1x + x = 0 0 + 2x2 + 7y + 3y2 = 0 + x 2x2 + 7y + 3y2 = 0 + x Remove the zero: 2x2 + 7y + 3y2 = x Add '-2x2' to each side of the equation. 2x2 + 7y + -2x2 + 3y2 = x + -2x2 Reorder the terms: 2x2 + -2x2 + 7y + 3y2 = x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 7y + 3y2 = x + -2x2 7y + 3y2 = x + -2x2 Add '-7y' to each side of the equation. 7y + -7y + 3y2 = x + -2x2 + -7y Combine like terms: 7y + -7y = 0 0 + 3y2 = x + -2x2 + -7y 3y2 = x + -2x2 + -7y Add '-3y2' to each side of the equation. 3y2 + -3y2 = x + -2x2 + -7y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = x + -2x2 + -7y + -3y2 Simplifying 0 = x + -2x2 + -7y + -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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