1n(x+2)+1nx=1n(x+20)

Solution for 1n(x+2)+1nx=1n(x+20) equation:

Simplifying
1n(x + 2) + 1nx = 1n(x + 20)

Reorder the terms:
1n(2 + x) + 1nx = 1n(x + 20)
(2 * 1n + x * 1n) + 1nx = 1n(x + 20)
(2n + 1nx) + 1nx = 1n(x + 20)

Combine like terms: 1nx + 1nx = 2nx
2n + 2nx = 1n(x + 20)

Reorder the terms:
2n + 2nx = 1n(20 + x)
2n + 2nx = (20 * 1n + x * 1n)
2n + 2nx = (20n + 1nx)

Solving
2n + 2nx = 20n + 1nx

Solving for variable 'n'.

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

Add '-20n' to each side of the equation.
2n + -20n + 2nx = 20n + -20n + 1nx

Combine like terms: 2n + -20n = -18n
-18n + 2nx = 20n + -20n + 1nx

Combine like terms: 20n + -20n = 0
-18n + 2nx = 0 + 1nx
-18n + 2nx = 1nx

Add '-1nx' to each side of the equation.
-18n + 2nx + -1nx = 1nx + -1nx

Combine like terms: 2nx + -1nx = 1nx
-18n + 1nx = 1nx + -1nx

Combine like terms: 1nx + -1nx = 0
-18n + 1nx = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-18 + 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 '(-18 + x)' equal to zero and attempt to solve:

Simplifying
-18 + x = 0

Solving
-18 + x = 0

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

Add '18' to each side of the equation.
-18 + 18 + x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + x = 0 + 18
x = 0 + 18

Combine like terms: 0 + 18 = 18
x = 18

Add '-1x' to each side of the equation.
x + -1x = 18 + -1x

Combine like terms: x + -1x = 0
0 = 18 + -1x

Simplifying
0 = 18 + -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}