In(x-3)+In(x+2)=In(x^2-2x)

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Solution for In(x-3)+In(x+2)=In(x^2-2x) equation: 


Simplifying
In(x + -3) + In(x + 2) = In(x2 + -2x)

Reorder the terms:
nI(-3 + x) + In(x + 2) = In(x2 + -2x)
(-3 * nI + x * nI) + In(x + 2) = In(x2 + -2x)
(-3nI + nxI) + In(x + 2) = In(x2 + -2x)

Reorder the terms:
-3nI + nxI + nI(2 + x) = In(x2 + -2x)
-3nI + nxI + (2 * nI + x * nI) = In(x2 + -2x)
-3nI + nxI + (2nI + nxI) = In(x2 + -2x)

Reorder the terms:
-3nI + 2nI + nxI + nxI = In(x2 + -2x)

Combine like terms: -3nI + 2nI = -1nI
-1nI + nxI + nxI = In(x2 + -2x)

Combine like terms: nxI + nxI = 2nxI
-1nI + 2nxI = In(x2 + -2x)

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

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

Solving for variable 'n'.

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

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

Combine like terms: 2nxI + 2nxI = 4nxI
-1nI + 4nxI = -2nxI + 2nxI + nx2I

Combine like terms: -2nxI + 2nxI = 0
-1nI + 4nxI = 0 + nx2I
-1nI + 4nxI = nx2I

Add '-1nx2I' to each side of the equation.
-1nI + 4nxI + -1nx2I = nx2I + -1nx2I

Combine like terms: nx2I + -1nx2I = 0
-1nI + 4nxI + -1nx2I = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(-1 + 4x + -1x2) = 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 '(-1 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1 + 4x + -1x2 = 0

Solving
-1 + 4x + -1x2 = 0

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

Add '1' to each side of the equation.
-1 + 4x + 1 + -1x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4x + -1x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x + -1x2 = 0 + 1
4x + -1x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4x + -1x2 = 1

Add '-4x' to each side of the equation.
4x + -4x + -1x2 = 1 + -4x

Combine like terms: 4x + -4x = 0
0 + -1x2 = 1 + -4x
-1x2 = 1 + -4x

Add 'x2' to each side of the equation.
-1x2 + x2 = 1 + -4x + x2

Combine like terms: -1x2 + x2 = 0
0 = 1 + -4x + x2

Simplifying
0 = 1 + -4x + x2

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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