2ln(x-1)+ln(2x+1)+ln(2)=ln(4x+2)+ln(x-3)+ln(x-3)

Solution for 2ln(x-1)+ln(2x+1)+ln(2)=ln(4x+2)+ln(x-3)+ln(x-3) equation:

Simplifying
2ln(x + -1) + ln(2x + 1) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Reorder the terms:
2ln(-1 + x) + ln(2x + 1) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)
(-1 * 2ln + x * 2ln) + ln(2x + 1) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)
(-2ln + 2lnx) + ln(2x + 1) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Reorder the terms:
-2ln + 2lnx + ln(1 + 2x) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)
-2ln + 2lnx + (1 * ln + 2x * ln) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)
-2ln + 2lnx + (1ln + 2lnx) + ln(2) = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Reorder the terms for easier multiplication:
-2ln + 2lnx + 1ln + 2lnx + 2ln = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Reorder the terms:
-2ln + 1ln + 2ln + 2lnx + 2lnx = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Combine like terms: -2ln + 1ln = -1ln
-1ln + 2ln + 2lnx + 2lnx = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Combine like terms: -1ln + 2ln = 1ln
1ln + 2lnx + 2lnx = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Combine like terms: 2lnx + 2lnx = 4lnx
1ln + 4lnx = ln(4x + 2) + ln(x + -3) + ln(x + -3)

Reorder the terms:
1ln + 4lnx = ln(2 + 4x) + ln(x + -3) + ln(x + -3)
1ln + 4lnx = (2 * ln + 4x * ln) + ln(x + -3) + ln(x + -3)
1ln + 4lnx = (2ln + 4lnx) + ln(x + -3) + ln(x + -3)

Reorder the terms:
1ln + 4lnx = 2ln + 4lnx + ln(-3 + x) + ln(x + -3)
1ln + 4lnx = 2ln + 4lnx + (-3 * ln + x * ln) + ln(x + -3)
1ln + 4lnx = 2ln + 4lnx + (-3ln + lnx) + ln(x + -3)

Reorder the terms:
1ln + 4lnx = 2ln + 4lnx + -3ln + lnx + ln(-3 + x)
1ln + 4lnx = 2ln + 4lnx + -3ln + lnx + (-3 * ln + x * ln)
1ln + 4lnx = 2ln + 4lnx + -3ln + lnx + (-3ln + lnx)

Reorder the terms:
1ln + 4lnx = 2ln + -3ln + -3ln + 4lnx + lnx + lnx

Combine like terms: 2ln + -3ln = -1ln
1ln + 4lnx = -1ln + -3ln + 4lnx + lnx + lnx

Combine like terms: -1ln + -3ln = -4ln
1ln + 4lnx = -4ln + 4lnx + lnx + lnx

Combine like terms: 4lnx + lnx = 5lnx
1ln + 4lnx = -4ln + 5lnx + lnx

Combine like terms: 5lnx + lnx = 6lnx
1ln + 4lnx = -4ln + 6lnx

Solving
1ln + 4lnx = -4ln + 6lnx

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
1ln + 4ln + 4lnx = -4ln + 4ln + 6lnx

Combine like terms: 1ln + 4ln = 5ln
5ln + 4lnx = -4ln + 4ln + 6lnx

Combine like terms: -4ln + 4ln = 0
5ln + 4lnx = 0 + 6lnx
5ln + 4lnx = 6lnx

Add '-6lnx' to each side of the equation.
5ln + 4lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 4lnx + -6lnx = -2lnx
5ln + -2lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
5ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -2x) = 0

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Add '2x' to each side of the equation.
-2x + 2x = -5 + 2x

Combine like terms: -2x + 2x = 0
0 = -5 + 2x

Simplifying
0 = -5 + 2x

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.