lnx+on(x-4)=ln(x+6)

Solution for lnx+on(x-4)=ln(x+6) equation:

Simplifying
lnx + on(x + -4) = ln(x + 6)

Reorder the terms:
lnx + no(-4 + x) = ln(x + 6)
lnx + (-4 * no + x * no) = ln(x + 6)
lnx + (-4no + nox) = ln(x + 6)

Reorder the terms:
lnx + -4no + nox = ln(6 + x)
lnx + -4no + nox = (6 * ln + x * ln)
lnx + -4no + nox = (6ln + lnx)

Add '-1lnx' to each side of the equation.
lnx + -4no + -1lnx + nox = 6ln + lnx + -1lnx

Reorder the terms:
lnx + -1lnx + -4no + nox = 6ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
0 + -4no + nox = 6ln + lnx + -1lnx
-4no + nox = 6ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-4no + nox = 6ln + 0
-4no + nox = 6ln

Solving
-4no + nox = 6ln

Solving for variable 'n'.

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

Add '-6ln' to each side of the equation.
-4no + -6ln + nox = 6ln + -6ln

Reorder the terms:
-6ln + -4no + nox = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-6ln + -4no + nox = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6l + -4o + ox) = 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 '(-6l + -4o + ox)' equal to zero and attempt to solve:

Simplifying
-6l + -4o + ox = 0

Solving
-6l + -4o + ox = 0

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

Add '6l' to each side of the equation.
-6l + -4o + 6l + ox = 0 + 6l

Reorder the terms:
-6l + 6l + -4o + ox = 0 + 6l

Combine like terms: -6l + 6l = 0
0 + -4o + ox = 0 + 6l
-4o + ox = 0 + 6l
Remove the zero:
-4o + ox = 6l

Add '4o' to each side of the equation.
-4o + 4o + ox = 6l + 4o

Combine like terms: -4o + 4o = 0
0 + ox = 6l + 4o
ox = 6l + 4o

Add '-1ox' to each side of the equation.
ox + -1ox = 6l + 4o + -1ox

Combine like terms: ox + -1ox = 0
0 = 6l + 4o + -1ox

Simplifying
0 = 6l + 4o + -1ox

The solution to this equation could not be determined.

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