n(x+5)=-ln(x-1)-ln(x+1)

Solution for n(x+5)=-ln(x-1)-ln(x+1) equation:

Simplifying
n(x + 5) = -1ln(x + -1) + -1ln(x + 1)

Reorder the terms:
n(5 + x) = -1ln(x + -1) + -1ln(x + 1)
(5 * n + x * n) = -1ln(x + -1) + -1ln(x + 1)
(5n + nx) = -1ln(x + -1) + -1ln(x + 1)

Reorder the terms:
5n + nx = -1ln(-1 + x) + -1ln(x + 1)
5n + nx = (-1 * -1ln + x * -1ln) + -1ln(x + 1)
5n + nx = (1ln + -1lnx) + -1ln(x + 1)

Reorder the terms:
5n + nx = 1ln + -1lnx + -1ln(1 + x)
5n + nx = 1ln + -1lnx + (1 * -1ln + x * -1ln)
5n + nx = 1ln + -1lnx + (-1ln + -1lnx)

Reorder the terms:
5n + nx = 1ln + -1ln + -1lnx + -1lnx

Combine like terms: 1ln + -1ln = 0
5n + nx = 0 + -1lnx + -1lnx
5n + nx = -1lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
5n + nx = -2lnx

Solving
5n + nx = -2lnx

Solving for variable 'n'.

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

Add '2lnx' to each side of the equation.
5n + 2lnx + nx = -2lnx + 2lnx

Reorder the terms:
2lnx + 5n + nx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
2lnx + 5n + nx = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(2lx + 5 + x) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(2lx + 5 + x)' equal to zero and attempt to solve:

Simplifying
2lx + 5 + x = 0

Reorder the terms:
5 + 2lx + x = 0

Solving
5 + 2lx + x = 0

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

Add '-5' to each side of the equation.
5 + 2lx + -5 + x = 0 + -5

Reorder the terms:
5 + -5 + 2lx + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2lx + x = 0 + -5
2lx + x = 0 + -5

Combine like terms: 0 + -5 = -5
2lx + x = -5

Add '-2lx' to each side of the equation.
2lx + -2lx + x = -5 + -2lx

Combine like terms: 2lx + -2lx = 0
0 + x = -5 + -2lx
x = -5 + -2lx

Add '-1x' to each side of the equation.
x + -1x = -5 + -2lx + -1x

Combine like terms: x + -1x = 0
0 = -5 + -2lx + -1x

Simplifying
0 = -5 + -2lx + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}