Ln(3x-5n)=ln(14+2n^2)

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Solution for Ln(3x-5n)=ln(14+2n^2) equation: 


Simplifying
Ln(3x + -5n) = ln(14 + 2n2)

Reorder the terms:
nL(-5n + 3x) = ln(14 + 2n2)
(-5n * nL + 3x * nL) = ln(14 + 2n2)

Reorder the terms:
(3nxL + -5n2L) = ln(14 + 2n2)
(3nxL + -5n2L) = ln(14 + 2n2)
3nxL + -5n2L = (14 * ln + 2n2 * ln)
3nxL + -5n2L = (14ln + 2ln3)

Solving
3nxL + -5n2L = 14ln + 2ln3

Solving for variable 'n'.

Reorder the terms:
-14ln + -2ln3 + 3nxL + -5n2L = 14ln + 2ln3 + -14ln + -2ln3

Reorder the terms:
-14ln + -2ln3 + 3nxL + -5n2L = 14ln + -14ln + 2ln3 + -2ln3

Combine like terms: 14ln + -14ln = 0
-14ln + -2ln3 + 3nxL + -5n2L = 0 + 2ln3 + -2ln3
-14ln + -2ln3 + 3nxL + -5n2L = 2ln3 + -2ln3

Combine like terms: 2ln3 + -2ln3 = 0
-14ln + -2ln3 + 3nxL + -5n2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-14l + -2ln2 + 3xL + -5nL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-14l + -2ln2 + 3xL + -5nL)' equal to zero and attempt to solve:

Simplifying
-14l + -2ln2 + 3xL + -5nL = 0

Reorder the terms:
-14l + -2ln2 + -5nL + 3xL = 0

Solving
-14l + -2ln2 + -5nL + 3xL = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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