In(x-1)+In(x+2)=In(6x-8)

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Solution for In(x-1)+In(x+2)=In(6x-8) equation: 


Simplifying
In(x + -1) + In(x + 2) = In(6x + -8)

Reorder the terms:
nI(-1 + x) + In(x + 2) = In(6x + -8)
(-1 * nI + x * nI) + In(x + 2) = In(6x + -8)
(-1nI + nxI) + In(x + 2) = In(6x + -8)

Reorder the terms:
-1nI + nxI + nI(2 + x) = In(6x + -8)
-1nI + nxI + (2 * nI + x * nI) = In(6x + -8)
-1nI + nxI + (2nI + nxI) = In(6x + -8)

Reorder the terms:
-1nI + 2nI + nxI + nxI = In(6x + -8)

Combine like terms: -1nI + 2nI = 1nI
1nI + nxI + nxI = In(6x + -8)

Combine like terms: nxI + nxI = 2nxI
1nI + 2nxI = In(6x + -8)

Reorder the terms:
1nI + 2nxI = nI(-8 + 6x)
1nI + 2nxI = (-8 * nI + 6x * nI)
1nI + 2nxI = (-8nI + 6nxI)

Solving
1nI + 2nxI = -8nI + 6nxI

Solving for variable 'n'.

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

Add '8nI' to each side of the equation.
1nI + 8nI + 2nxI = -8nI + 8nI + 6nxI

Combine like terms: 1nI + 8nI = 9nI
9nI + 2nxI = -8nI + 8nI + 6nxI

Combine like terms: -8nI + 8nI = 0
9nI + 2nxI = 0 + 6nxI
9nI + 2nxI = 6nxI

Add '-6nxI' to each side of the equation.
9nI + 2nxI + -6nxI = 6nxI + -6nxI

Combine like terms: 2nxI + -6nxI = -4nxI
9nI + -4nxI = 6nxI + -6nxI

Combine like terms: 6nxI + -6nxI = 0
9nI + -4nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(9 + -4x) = 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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Add '4x' to each side of the equation.
-4x + 4x = -9 + 4x

Combine like terms: -4x + 4x = 0
0 = -9 + 4x

Simplifying
0 = -9 + 4x

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.

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