1n(5x+1)=1n(4x-1)

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Solution for 1n(5x+1)=1n(4x-1) equation: 


Simplifying
1n(5x + 1) = 1n(4x + -1)

Reorder the terms:
1n(1 + 5x) = 1n(4x + -1)
(1 * 1n + 5x * 1n) = 1n(4x + -1)
(1n + 5nx) = 1n(4x + -1)

Reorder the terms:
1n + 5nx = 1n(-1 + 4x)
1n + 5nx = (-1 * 1n + 4x * 1n)
1n + 5nx = (-1n + 4nx)

Solving
1n + 5nx = -1n + 4nx

Solving for variable 'n'.

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

Add 'n' to each side of the equation.
1n + n + 5nx = -1n + n + 4nx

Combine like terms: 1n + n = 2n
2n + 5nx = -1n + n + 4nx

Combine like terms: -1n + n = 0
2n + 5nx = 0 + 4nx
2n + 5nx = 4nx

Add '-4nx' to each side of the equation.
2n + 5nx + -4nx = 4nx + -4nx

Combine like terms: 5nx + -4nx = 1nx
2n + 1nx = 4nx + -4nx

Combine like terms: 4nx + -4nx = 0
2n + 1nx = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

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

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

Simplifying
0 = -2 + -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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