1n(5x-5)=1n(2x+3)+1n(15)

Solution for 1n(5x-5)=1n(2x+3)+1n(15) equation:

Simplifying
1n(5x + -5) = 1n(2x + 3) + 1n(15)

Reorder the terms:
1n(-5 + 5x) = 1n(2x + 3) + 1n(15)
(-5 * 1n + 5x * 1n) = 1n(2x + 3) + 1n(15)
(-5n + 5nx) = 1n(2x + 3) + 1n(15)

Reorder the terms:
-5n + 5nx = 1n(3 + 2x) + 1n(15)
-5n + 5nx = (3 * 1n + 2x * 1n) + 1n(15)
-5n + 5nx = (3n + 2nx) + 1n(15)

Reorder the terms for easier multiplication:
-5n + 5nx = 3n + 2nx + 1 * 15n

Multiply 1 * 15
-5n + 5nx = 3n + 2nx + 15n

Reorder the terms:
-5n + 5nx = 3n + 15n + 2nx

Combine like terms: 3n + 15n = 18n
-5n + 5nx = 18n + 2nx

Solving
-5n + 5nx = 18n + 2nx

Solving for variable 'n'.

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

Add '-18n' to each side of the equation.
-5n + -18n + 5nx = 18n + -18n + 2nx

Combine like terms: -5n + -18n = -23n
-23n + 5nx = 18n + -18n + 2nx

Combine like terms: 18n + -18n = 0
-23n + 5nx = 0 + 2nx
-23n + 5nx = 2nx

Add '-2nx' to each side of the equation.
-23n + 5nx + -2nx = 2nx + -2nx

Combine like terms: 5nx + -2nx = 3nx
-23n + 3nx = 2nx + -2nx

Combine like terms: 2nx + -2nx = 0
-23n + 3nx = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-23 + 3x) = 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 '(-23 + 3x)' equal to zero and attempt to solve:

Simplifying
-23 + 3x = 0

Solving
-23 + 3x = 0

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

Add '23' to each side of the equation.
-23 + 23 + 3x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 3x = 0 + 23
3x = 0 + 23

Combine like terms: 0 + 23 = 23
3x = 23

Add '-3x' to each side of the equation.
3x + -3x = 23 + -3x

Combine like terms: 3x + -3x = 0
0 = 23 + -3x

Simplifying
0 = 23 + -3x

The solution to this equation could not be determined.

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