Ln(2x+5)=ln(3x-3)

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


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

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

Reorder the terms:
5nL + 2nxL = ln(-3 + 3x)
5nL + 2nxL = (-3 * ln + 3x * ln)
5nL + 2nxL = (-3ln + 3lnx)

Solving
5nL + 2nxL = -3ln + 3lnx

Solving for variable 'n'.

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

Add '3ln' to each side of the equation.
5nL + 3ln + 2nxL = -3ln + 3ln + 3lnx

Reorder the terms:
3ln + 5nL + 2nxL = -3ln + 3ln + 3lnx

Combine like terms: -3ln + 3ln = 0
3ln + 5nL + 2nxL = 0 + 3lnx
3ln + 5nL + 2nxL = 3lnx

Add '-3lnx' to each side of the equation.
3ln + 5nL + -3lnx + 2nxL = 3lnx + -3lnx

Reorder the terms:
3ln + -3lnx + 5nL + 2nxL = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
3ln + -3lnx + 5nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3l + -3lx + 5L + 2xL) = 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 '(3l + -3lx + 5L + 2xL)' equal to zero and attempt to solve:

Simplifying
3l + -3lx + 5L + 2xL = 0

Reorder the terms:
5L + 3l + -3lx + 2xL = 0

Solving
5L + 3l + -3lx + 2xL = 0

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

Add '-5L' to each side of the equation.
5L + 3l + -3lx + -5L + 2xL = 0 + -5L

Reorder the terms:
5L + -5L + 3l + -3lx + 2xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + 3l + -3lx + 2xL = 0 + -5L
3l + -3lx + 2xL = 0 + -5L
Remove the zero:
3l + -3lx + 2xL = -5L

Add '-3l' to each side of the equation.
3l + -3lx + -3l + 2xL = -5L + -3l

Reorder the terms:
3l + -3l + -3lx + 2xL = -5L + -3l

Combine like terms: 3l + -3l = 0
0 + -3lx + 2xL = -5L + -3l
-3lx + 2xL = -5L + -3l

Add '3lx' to each side of the equation.
-3lx + 3lx + 2xL = -5L + -3l + 3lx

Combine like terms: -3lx + 3lx = 0
0 + 2xL = -5L + -3l + 3lx
2xL = -5L + -3l + 3lx

Add '-2xL' to each side of the equation.
2xL + -2xL = -5L + -3l + 3lx + -2xL

Combine like terms: 2xL + -2xL = 0
0 = -5L + -3l + 3lx + -2xL

Simplifying
0 = -5L + -3l + 3lx + -2xL

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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