In(x-2)+in(2x-3)=2Inx

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


Simplifying
In(x + -2) + in(2x + -3) = 2Inx

Reorder the terms:
nI(-2 + x) + in(2x + -3) = 2Inx
(-2 * nI + x * nI) + in(2x + -3) = 2Inx
(-2nI + nxI) + in(2x + -3) = 2Inx

Reorder the terms:
-2nI + nxI + in(-3 + 2x) = 2Inx
-2nI + nxI + (-3 * in + 2x * in) = 2Inx
-2nI + nxI + (-3in + 2inx) = 2Inx

Reorder the terms:
-3in + 2inx + -2nI + nxI = 2Inx

Solving
-3in + 2inx + -2nI + nxI = 2nxI

Solving for variable 'i'.

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

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

Combine like terms: -2nI + 2nI = 0
-3in + 2inx + 0 + nxI = 2nI + 2nxI
-3in + 2inx + nxI = 2nI + 2nxI

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

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

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

Reorder the terms:
-3in + 2inx + -2nI + -1nxI = 2nI + -2nI + 1nxI + -1nxI

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

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

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

Simplifying
-3i + 2ix + -2I + -1xI = 0

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

Solving
-2I + -3i + 2ix + -1xI = 0

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

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

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

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

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

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

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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