Ln(3x+6)=ln(2x-1)

Solution for Ln(3x+6)=ln(2x-1) equation:

Simplifying
Ln(3x + 6) = ln(2x + -1)

Reorder the terms:
nL(6 + 3x) = ln(2x + -1)
(6 * nL + 3x * nL) = ln(2x + -1)
(6nL + 3nxL) = ln(2x + -1)

Reorder the terms:
6nL + 3nxL = ln(-1 + 2x)
6nL + 3nxL = (-1 * ln + 2x * ln)
6nL + 3nxL = (-1ln + 2lnx)

Solving
6nL + 3nxL = -1ln + 2lnx

Solving for variable 'n'.

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

Add 'ln' to each side of the equation.
6nL + ln + 3nxL = -1ln + ln + 2lnx

Reorder the terms:
ln + 6nL + 3nxL = -1ln + ln + 2lnx

Combine like terms: -1ln + ln = 0
ln + 6nL + 3nxL = 0 + 2lnx
ln + 6nL + 3nxL = 2lnx

Add '-2lnx' to each side of the equation.
ln + 6nL + -2lnx + 3nxL = 2lnx + -2lnx

Reorder the terms:
ln + -2lnx + 6nL + 3nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
ln + -2lnx + 6nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(l + -2lx + 6L + 3xL) = 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 '(l + -2lx + 6L + 3xL)' equal to zero and attempt to solve:

Simplifying
l + -2lx + 6L + 3xL = 0

Reorder the terms:
6L + l + -2lx + 3xL = 0

Solving
6L + l + -2lx + 3xL = 0

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

Add '-6L' to each side of the equation.
6L + l + -2lx + -6L + 3xL = 0 + -6L

Reorder the terms:
6L + -6L + l + -2lx + 3xL = 0 + -6L

Combine like terms: 6L + -6L = 0
0 + l + -2lx + 3xL = 0 + -6L
l + -2lx + 3xL = 0 + -6L
Remove the zero:
l + -2lx + 3xL = -6L

Add '-1l' to each side of the equation.
l + -2lx + -1l + 3xL = -6L + -1l

Reorder the terms:
l + -1l + -2lx + 3xL = -6L + -1l

Combine like terms: l + -1l = 0
0 + -2lx + 3xL = -6L + -1l
-2lx + 3xL = -6L + -1l

Add '2lx' to each side of the equation.
-2lx + 2lx + 3xL = -6L + -1l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 3xL = -6L + -1l + 2lx
3xL = -6L + -1l + 2lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -6L + -1l + 2lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -6L + -1l + 2lx + -3xL

Simplifying
0 = -6L + -1l + 2lx + -3xL

The solution to this equation could not be determined.

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