ln(3n+7)=ln(-3n-5)

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Solution for ln(3n+7)=ln(-3n-5) equation: 


Simplifying
ln(3n + 7) = ln(-3n + -5)

Reorder the terms:
ln(7 + 3n) = ln(-3n + -5)
(7 * ln + 3n * ln) = ln(-3n + -5)
(7ln + 3ln2) = ln(-3n + -5)

Reorder the terms:
7ln + 3ln2 = ln(-5 + -3n)
7ln + 3ln2 = (-5 * ln + -3n * ln)
7ln + 3ln2 = (-5ln + -3ln2)

Solving
7ln + 3ln2 = -5ln + -3ln2

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
7ln + 5ln + 3ln2 = -5ln + 5ln + -3ln2

Combine like terms: 7ln + 5ln = 12ln
12ln + 3ln2 = -5ln + 5ln + -3ln2

Combine like terms: -5ln + 5ln = 0
12ln + 3ln2 = 0 + -3ln2
12ln + 3ln2 = -3ln2

Add '3ln2' to each side of the equation.
12ln + 3ln2 + 3ln2 = -3ln2 + 3ln2

Combine like terms: 3ln2 + 3ln2 = 6ln2
12ln + 6ln2 = -3ln2 + 3ln2

Combine like terms: -3ln2 + 3ln2 = 0
12ln + 6ln2 = 0

Factor out the Greatest Common Factor (GCF), '6ln'.
6ln(2 + n) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 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 '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Add '-1n' to each side of the equation.
n + -1n = -2 + -1n

Combine like terms: n + -1n = 0
0 = -2 + -1n

Simplifying
0 = -2 + -1n

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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