(8y+10x)dx+(5y+7x)dy=0

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Solution for (8y+10x)dx+(5y+7x)dy=0 equation:


Simplifying
(8y + 10x) * dx + (5y + 7x) * dy = 0

Reorder the terms:
(10x + 8y) * dx + (5y + 7x) * dy = 0

Reorder the terms for easier multiplication:
dx(10x + 8y) + (5y + 7x) * dy = 0
(10x * dx + 8y * dx) + (5y + 7x) * dy = 0

Reorder the terms:
(8dxy + 10dx2) + (5y + 7x) * dy = 0
(8dxy + 10dx2) + (5y + 7x) * dy = 0

Reorder the terms:
8dxy + 10dx2 + (7x + 5y) * dy = 0

Reorder the terms for easier multiplication:
8dxy + 10dx2 + dy(7x + 5y) = 0
8dxy + 10dx2 + (7x * dy + 5y * dy) = 0
8dxy + 10dx2 + (7dxy + 5dy2) = 0

Reorder the terms:
8dxy + 7dxy + 10dx2 + 5dy2 = 0

Combine like terms: 8dxy + 7dxy = 15dxy
15dxy + 10dx2 + 5dy2 = 0

Solving
15dxy + 10dx2 + 5dy2 = 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), '5d'.
5d(3xy + 2x2 + y2) = 0

Factor a trinomial.
5d((2x + y)(x + y)) = 0

Ignore the factor 5.

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 + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 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 + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y 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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