1n(x+1)=1n(3x)

Solution for 1n(x+1)=1n(3x) equation:

Simplifying
1n(x + 1) = 1n(3x)

Reorder the terms:
1n(1 + x) = 1n(3x)
(1 * 1n + x * 1n) = 1n(3x)
(1n + 1nx) = 1n(3x)

Remove parenthesis around (3x)
1n + 1nx = 1n * 3x

Reorder the terms for easier multiplication:
1n + 1nx = 1 * 3n * x

Multiply 1 * 3
1n + 1nx = 3n * x

Multiply n * x
1n + 1nx = 3nx

Solving
1n + 1nx = 3nx

Solving for variable 'n'.

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

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

Combine like terms: 1nx + -3nx = -2nx
1n + -2nx = 3nx + -3nx

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + -2x) = 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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 2x

The solution to this equation could not be determined.

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