ln(x+3)+l(x-1)=0

Solution for ln(x+3)+l(x-1)=0 equation:

Simplifying
ln(x + 3) + l(x + -1) = 0

Reorder the terms:
ln(3 + x) + l(x + -1) = 0
(3 * ln + x * ln) + l(x + -1) = 0
(3ln + lnx) + l(x + -1) = 0

Reorder the terms:
3ln + lnx + l(-1 + x) = 0
3ln + lnx + (-1 * l + x * l) = 0
3ln + lnx + (-1l + lx) = 0

Reorder the terms:
-1l + 3ln + lnx + lx = 0

Solving
-1l + 3ln + lnx + lx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'l'.
l(-1 + 3n + nx + x) = 0

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

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0
Subproblem 2
Set the factor '(-1 + 3n + nx + x)' equal to zero and attempt to solve:

Simplifying
-1 + 3n + nx + x = 0

Solving
-1 + 3n + nx + x = 0

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

Add '1' to each side of the equation.
-1 + 3n + nx + 1 + x = 0 + 1

Reorder the terms:
-1 + 1 + 3n + nx + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3n + nx + x = 0 + 1
3n + nx + x = 0 + 1

Combine like terms: 0 + 1 = 1
3n + nx + x = 1

Add '-3n' to each side of the equation.
3n + nx + -3n + x = 1 + -3n

Reorder the terms:
3n + -3n + nx + x = 1 + -3n

Combine like terms: 3n + -3n = 0
0 + nx + x = 1 + -3n
nx + x = 1 + -3n

Add '-1nx' to each side of the equation.
nx + -1nx + x = 1 + -3n + -1nx

Combine like terms: nx + -1nx = 0
0 + x = 1 + -3n + -1nx
x = 1 + -3n + -1nx

Add '-1x' to each side of the equation.
x + -1x = 1 + -3n + -1nx + -1x

Combine like terms: x + -1x = 0
0 = 1 + -3n + -1nx + -1x

Simplifying
0 = 1 + -3n + -1nx + -1x

The solution to this equation could not be determined.

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