2In(x+1)=In(x^2-1)+in(5)

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Solution for 2In(x+1)=In(x^2-1)+in(5) equation: 


Simplifying
2In(x + 1) = In(x2 + -1) + in(5)

Reorder the terms:
2nI(1 + x) = In(x2 + -1) + in(5)
(1 * 2nI + x * 2nI) = In(x2 + -1) + in(5)
(2nI + 2nxI) = In(x2 + -1) + in(5)

Reorder the terms:
2nI + 2nxI = nI(-1 + x2) + in(5)
2nI + 2nxI = (-1 * nI + x2 * nI) + in(5)
2nI + 2nxI = (-1nI + nx2I) + in(5)

Reorder the terms for easier multiplication:
2nI + 2nxI = -1nI + nx2I + 5in

Reorder the terms:
2nI + 2nxI = 5in + -1nI + nx2I

Solving
2nI + 2nxI = 5in + -1nI + nx2I

Solving for variable 'n'.

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

Add '-5in' to each side of the equation.
2nI + -5in + 2nxI = 5in + -1nI + -5in + nx2I

Reorder the terms:
-5in + 2nI + 2nxI = 5in + -1nI + -5in + nx2I

Reorder the terms:
-5in + 2nI + 2nxI = 5in + -5in + -1nI + nx2I

Combine like terms: 5in + -5in = 0
-5in + 2nI + 2nxI = 0 + -1nI + nx2I
-5in + 2nI + 2nxI = -1nI + nx2I

Add 'nI' to each side of the equation.
-5in + 2nI + nI + 2nxI = -1nI + nI + nx2I

Combine like terms: 2nI + nI = 3nI
-5in + 3nI + 2nxI = -1nI + nI + nx2I

Combine like terms: -1nI + nI = 0
-5in + 3nI + 2nxI = 0 + nx2I
-5in + 3nI + 2nxI = nx2I

Add '-1nx2I' to each side of the equation.
-5in + 3nI + 2nxI + -1nx2I = nx2I + -1nx2I

Combine like terms: nx2I + -1nx2I = 0
-5in + 3nI + 2nxI + -1nx2I = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5i + 3I + 2xI + -1x2I) = 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 '(-5i + 3I + 2xI + -1x2I)' equal to zero and attempt to solve:

Simplifying
-5i + 3I + 2xI + -1x2I = 0

Reorder the terms:
3I + -5i + 2xI + -1x2I = 0

Solving
3I + -5i + 2xI + -1x2I = 0

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

Add '-3I' to each side of the equation.
3I + -5i + 2xI + -3I + -1x2I = 0 + -3I

Reorder the terms:
3I + -3I + -5i + 2xI + -1x2I = 0 + -3I

Combine like terms: 3I + -3I = 0
0 + -5i + 2xI + -1x2I = 0 + -3I
-5i + 2xI + -1x2I = 0 + -3I
Remove the zero:
-5i + 2xI + -1x2I = -3I

Add '5i' to each side of the equation.
-5i + 2xI + 5i + -1x2I = -3I + 5i

Reorder the terms:
-5i + 5i + 2xI + -1x2I = -3I + 5i

Combine like terms: -5i + 5i = 0
0 + 2xI + -1x2I = -3I + 5i
2xI + -1x2I = -3I + 5i

Add '-2xI' to each side of the equation.
2xI + -2xI + -1x2I = -3I + 5i + -2xI

Combine like terms: 2xI + -2xI = 0
0 + -1x2I = -3I + 5i + -2xI
-1x2I = -3I + 5i + -2xI

Add 'x2I' to each side of the equation.
-1x2I + x2I = -3I + 5i + -2xI + x2I

Combine like terms: -1x2I + x2I = 0
0 = -3I + 5i + -2xI + x2I

Simplifying
0 = -3I + 5i + -2xI + x2I

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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