In(2x-3)-in(x+1)=2inx

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Solution for In(2x-3)-in(x+1)=2inx equation:


Simplifying
In(2x + -3) + -1in(x + 1) = 2inx

Reorder the terms:
nI(-3 + 2x) + -1in(x + 1) = 2inx
(-3 * nI + 2x * nI) + -1in(x + 1) = 2inx
(-3nI + 2nxI) + -1in(x + 1) = 2inx

Reorder the terms:
-3nI + 2nxI + -1in(1 + x) = 2inx
-3nI + 2nxI + (1 * -1in + x * -1in) = 2inx
-3nI + 2nxI + (-1in + -1inx) = 2inx

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

Solving
-1in + -1inx + -3nI + 2nxI = 2inx

Solving for variable 'i'.

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

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

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

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

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

Add '3nI' to each side of the equation.
-1in + -3inx + -3nI + 3nI + 2nxI = 0 + 3nI

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1i + -3ix + -3I + 2xI) = 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 '(-1i + -3ix + -3I + 2xI)' equal to zero and attempt to solve: Simplifying -1i + -3ix + -3I + 2xI = 0 Reorder the terms: -3I + -1i + -3ix + 2xI = 0 Solving -3I + -1i + -3ix + 2xI = 0 Move all terms containing i to the left, all other terms to the right. Add '3I' to each side of the equation. -3I + -1i + -3ix + 3I + 2xI = 0 + 3I Reorder the terms: -3I + 3I + -1i + -3ix + 2xI = 0 + 3I Combine like terms: -3I + 3I = 0 0 + -1i + -3ix + 2xI = 0 + 3I -1i + -3ix + 2xI = 0 + 3I Remove the zero: -1i + -3ix + 2xI = 3I Add '-2xI' to each side of the equation. -1i + -3ix + 2xI + -2xI = 3I + -2xI Combine like terms: 2xI + -2xI = 0 -1i + -3ix + 0 = 3I + -2xI -1i + -3ix = 3I + -2xI 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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