In(x+3)-In(x-3)=In(x)

Solution for In(x+3)-In(x-3)=In(x) equation:

Simplifying
In(x + 3) + -1In(x + -3) = In(x)

Reorder the terms:
nI(3 + x) + -1In(x + -3) = In(x)
(3 * nI + x * nI) + -1In(x + -3) = In(x)
(3nI + nxI) + -1In(x + -3) = In(x)

Reorder the terms:
3nI + nxI + -1nI(-3 + x) = In(x)
3nI + nxI + (-3 * -1nI + x * -1nI) = In(x)
3nI + nxI + (3nI + -1nxI) = In(x)

Reorder the terms:
3nI + 3nI + nxI + -1nxI = In(x)

Combine like terms: 3nI + 3nI = 6nI
6nI + nxI + -1nxI = In(x)

Combine like terms: nxI + -1nxI = 0
6nI + 0 = In(x)
6nI = In(x)

Multiply nI * x
6nI = nxI

Solving
6nI = nxI

Solving for variable 'n'.

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

Add '-1nxI' to each side of the equation.
6nI + -1nxI = nxI + -1nxI

Combine like terms: nxI + -1nxI = 0
6nI + -1nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(6 + -1x) = 0

Subproblem 1
Set the factor 'nI' equal to zero and attempt to solve:

Simplifying
nI = 0

Solving
nI = 0

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

Simplifying
nI = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Add 'x' to each side of the equation.
-1x + x = -6 + x

Combine like terms: -1x + x = 0
0 = -6 + x

Simplifying
0 = -6 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.