lm(2x-3)-ln(x+5)=0

Solution for lm(2x-3)-ln(x+5)=0 equation:

Simplifying
lm(2x + -3) + -1ln(x + 5) = 0

Reorder the terms:
lm(-3 + 2x) + -1ln(x + 5) = 0
(-3 * lm + 2x * lm) + -1ln(x + 5) = 0
(-3lm + 2lmx) + -1ln(x + 5) = 0

Reorder the terms:
-3lm + 2lmx + -1ln(5 + x) = 0
-3lm + 2lmx + (5 * -1ln + x * -1ln) = 0
-3lm + 2lmx + (-5ln + -1lnx) = 0

Solving
-3lm + 2lmx + -5ln + -1lnx = 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(-3m + 2mx + -5n + -1nx) = 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 '(-3m + 2mx + -5n + -1nx)' equal to zero and attempt to solve:

Simplifying
-3m + 2mx + -5n + -1nx = 0

Solving
-3m + 2mx + -5n + -1nx = 0

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

Add '3m' to each side of the equation.
-3m + 2mx + -5n + 3m + -1nx = 0 + 3m

Reorder the terms:
-3m + 3m + 2mx + -5n + -1nx = 0 + 3m

Combine like terms: -3m + 3m = 0
0 + 2mx + -5n + -1nx = 0 + 3m
2mx + -5n + -1nx = 0 + 3m
Remove the zero:
2mx + -5n + -1nx = 3m

Add '-2mx' to each side of the equation.
2mx + -5n + -2mx + -1nx = 3m + -2mx

Reorder the terms:
2mx + -2mx + -5n + -1nx = 3m + -2mx

Combine like terms: 2mx + -2mx = 0
0 + -5n + -1nx = 3m + -2mx
-5n + -1nx = 3m + -2mx

Add '5n' to each side of the equation.
-5n + 5n + -1nx = 3m + -2mx + 5n

Combine like terms: -5n + 5n = 0
0 + -1nx = 3m + -2mx + 5n
-1nx = 3m + -2mx + 5n

Add 'nx' to each side of the equation.
-1nx + nx = 3m + -2mx + 5n + nx

Combine like terms: -1nx + nx = 0
0 = 3m + -2mx + 5n + nx

Simplifying
0 = 3m + -2mx + 5n + nx

The solution to this equation could not be determined.

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