1n(3x+1)=1n(2x-8)

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Solution for 1n(3x+1)=1n(2x-8) equation: 


Simplifying
1n(3x + 1) = 1n(2x + -8)

Reorder the terms:
1n(1 + 3x) = 1n(2x + -8)
(1 * 1n + 3x * 1n) = 1n(2x + -8)
(1n + 3nx) = 1n(2x + -8)

Reorder the terms:
1n + 3nx = 1n(-8 + 2x)
1n + 3nx = (-8 * 1n + 2x * 1n)
1n + 3nx = (-8n + 2nx)

Solving
1n + 3nx = -8n + 2nx

Solving for variable 'n'.

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

Add '8n' to each side of the equation.
1n + 8n + 3nx = -8n + 8n + 2nx

Combine like terms: 1n + 8n = 9n
9n + 3nx = -8n + 8n + 2nx

Combine like terms: -8n + 8n = 0
9n + 3nx = 0 + 2nx
9n + 3nx = 2nx

Add '-2nx' to each side of the equation.
9n + 3nx + -2nx = 2nx + -2nx

Combine like terms: 3nx + -2nx = 1nx
9n + 1nx = 2nx + -2nx

Combine like terms: 2nx + -2nx = 0
9n + 1nx = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(9 + 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 '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Add '-1x' to each side of the equation.
x + -1x = -9 + -1x

Combine like terms: x + -1x = 0
0 = -9 + -1x

Simplifying
0 = -9 + -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}

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