ln(-5y+8)-ln(y+5)=ln(-8y-12)

Solution for ln(-5y+8)-ln(y+5)=ln(-8y-12) equation:

Simplifying
ln(-5y + 8) + -1ln(y + 5) = ln(-8y + -12)

Reorder the terms:
ln(8 + -5y) + -1ln(y + 5) = ln(-8y + -12)
(8 * ln + -5y * ln) + -1ln(y + 5) = ln(-8y + -12)
(8ln + -5lny) + -1ln(y + 5) = ln(-8y + -12)

Reorder the terms:
8ln + -5lny + -1ln(5 + y) = ln(-8y + -12)
8ln + -5lny + (5 * -1ln + y * -1ln) = ln(-8y + -12)
8ln + -5lny + (-5ln + -1lny) = ln(-8y + -12)

Reorder the terms:
8ln + -5ln + -5lny + -1lny = ln(-8y + -12)

Combine like terms: 8ln + -5ln = 3ln
3ln + -5lny + -1lny = ln(-8y + -12)

Combine like terms: -5lny + -1lny = -6lny
3ln + -6lny = ln(-8y + -12)

Reorder the terms:
3ln + -6lny = ln(-12 + -8y)
3ln + -6lny = (-12 * ln + -8y * ln)
3ln + -6lny = (-12ln + -8lny)

Solving
3ln + -6lny = -12ln + -8lny

Solving for variable 'l'.

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

Add '12ln' to each side of the equation.
3ln + 12ln + -6lny = -12ln + 12ln + -8lny

Combine like terms: 3ln + 12ln = 15ln
15ln + -6lny = -12ln + 12ln + -8lny

Combine like terms: -12ln + 12ln = 0
15ln + -6lny = 0 + -8lny
15ln + -6lny = -8lny

Add '8lny' to each side of the equation.
15ln + -6lny + 8lny = -8lny + 8lny

Combine like terms: -6lny + 8lny = 2lny
15ln + 2lny = -8lny + 8lny

Combine like terms: -8lny + 8lny = 0
15ln + 2lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(15 + 2y) = 0

Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(15 + 2y)' equal to zero and attempt to solve:

Simplifying
15 + 2y = 0

Solving
15 + 2y = 0

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

Add '-15' to each side of the equation.
15 + -15 + 2y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2y = 0 + -15
2y = 0 + -15

Combine like terms: 0 + -15 = -15
2y = -15

Add '-2y' to each side of the equation.
2y + -2y = -15 + -2y

Combine like terms: 2y + -2y = 0
0 = -15 + -2y

Simplifying
0 = -15 + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.