In(x-1)-in(x+1)=in(x+5)

Solution for In(x-1)-in(x+1)=in(x+5) equation:

Simplifying
In(x + -1) + -1in(x + 1) = in(x + 5)

Reorder the terms:
nI(-1 + x) + -1in(x + 1) = in(x + 5)
(-1 * nI + x * nI) + -1in(x + 1) = in(x + 5)
(-1nI + nxI) + -1in(x + 1) = in(x + 5)

Reorder the terms:
-1nI + nxI + -1in(1 + x) = in(x + 5)
-1nI + nxI + (1 * -1in + x * -1in) = in(x + 5)
-1nI + nxI + (-1in + -1inx) = in(x + 5)

Reorder the terms:
-1in + -1inx + -1nI + nxI = in(x + 5)

Reorder the terms:
-1in + -1inx + -1nI + nxI = in(5 + x)
-1in + -1inx + -1nI + nxI = (5 * in + x * in)
-1in + -1inx + -1nI + nxI = (5in + inx)

Solving
-1in + -1inx + -1nI + nxI = 5in + inx

Solving for variable 'i'.

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

Add '-5in' to each side of the equation.
-1in + -1inx + -1nI + -5in + nxI = 5in + -5in + inx

Reorder the terms:
-1in + -5in + -1inx + -1nI + nxI = 5in + -5in + inx

Combine like terms: -1in + -5in = -6in
-6in + -1inx + -1nI + nxI = 5in + -5in + inx

Combine like terms: 5in + -5in = 0
-6in + -1inx + -1nI + nxI = 0 + inx
-6in + -1inx + -1nI + nxI = inx

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

Reorder the terms:
-6in + -1inx + -1inx + -1nI + nxI = inx + -1inx

Combine like terms: -1inx + -1inx = -2inx
-6in + -2inx + -1nI + nxI = inx + -1inx

Combine like terms: inx + -1inx = 0
-6in + -2inx + -1nI + nxI = 0

Add 'nI' to each side of the equation.
-6in + -2inx + -1nI + nI + nxI = 0 + nI

Combine like terms: -1nI + nI = 0
-6in + -2inx + 0 + nxI = 0 + nI
-6in + -2inx + nxI = 0 + nI
Remove the zero:
-6in + -2inx + nxI = nI

Add '-1nxI' to each side of the equation.
-6in + -2inx + nxI + -1nxI = nI + -1nxI

Combine like terms: nxI + -1nxI = 0
-6in + -2inx + 0 = nI + -1nxI
-6in + -2inx = nI + -1nxI

Reorder the terms:
-6in + -2inx + -1nI + nxI = nI + -1nI + -1nxI + nxI

Combine like terms: nI + -1nI = 0
-6in + -2inx + -1nI + nxI = 0 + -1nxI + nxI
-6in + -2inx + -1nI + nxI = -1nxI + nxI

Combine like terms: -1nxI + nxI = 0
-6in + -2inx + -1nI + nxI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6i + -2ix + -1I + xI) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-6i + -2ix + -1I + xI)' equal to zero and attempt to solve:

Simplifying
-6i + -2ix + -1I + xI = 0

Reorder the terms:
-1I + -6i + -2ix + xI = 0

Solving
-1I + -6i + -2ix + xI = 0

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

Add 'I' to each side of the equation.
-1I + -6i + -2ix + I + xI = 0 + I

Reorder the terms:
-1I + I + -6i + -2ix + xI = 0 + I

Combine like terms: -1I + I = 0
0 + -6i + -2ix + xI = 0 + I
-6i + -2ix + xI = 0 + I
Remove the zero:
-6i + -2ix + xI = I

Add '-1xI' to each side of the equation.
-6i + -2ix + xI + -1xI = I + -1xI

Combine like terms: xI + -1xI = 0
-6i + -2ix + 0 = I + -1xI
-6i + -2ix = I + -1xI

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.