In(4X+7)=In(3X-5)

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Solution for In(4X+7)=In(3X-5) equation: 


Simplifying
In(4X + 7) = In(3X + -5)

Reorder the terms:
nI(7 + 4X) = In(3X + -5)
(7 * nI + 4X * nI) = In(3X + -5)
(7nI + 4nIX) = In(3X + -5)

Reorder the terms:
7nI + 4nIX = nI(-5 + 3X)
7nI + 4nIX = (-5 * nI + 3X * nI)
7nI + 4nIX = (-5nI + 3nIX)

Solving
7nI + 4nIX = -5nI + 3nIX

Solving for variable 'n'.

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

Add '5nI' to each side of the equation.
7nI + 5nI + 4nIX = -5nI + 5nI + 3nIX

Combine like terms: 7nI + 5nI = 12nI
12nI + 4nIX = -5nI + 5nI + 3nIX

Combine like terms: -5nI + 5nI = 0
12nI + 4nIX = 0 + 3nIX
12nI + 4nIX = 3nIX

Add '-3nIX' to each side of the equation.
12nI + 4nIX + -3nIX = 3nIX + -3nIX

Combine like terms: 4nIX + -3nIX = 1nIX
12nI + 1nIX = 3nIX + -3nIX

Combine like terms: 3nIX + -3nIX = 0
12nI + 1nIX = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(12 + X) = 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 '(12 + X)' equal to zero and attempt to solve:

Simplifying
12 + X = 0

Solving
12 + X = 0

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

Add '-12' to each side of the equation.
12 + -12 + X = 0 + -12

Combine like terms: 12 + -12 = 0
0 + X = 0 + -12
X = 0 + -12

Combine like terms: 0 + -12 = -12
X = -12

Add '-1X' to each side of the equation.
X + -1X = -12 + -1X

Combine like terms: X + -1X = 0
0 = -12 + -1X

Simplifying
0 = -12 + -1X

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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