n(9x+33)=ln(6x+12)

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Solution for n(9x+33)=ln(6x+12) equation: 


Simplifying
n(9x + 33) = ln(6x + 12)

Reorder the terms:
n(33 + 9x) = ln(6x + 12)
(33 * n + 9x * n) = ln(6x + 12)
(33n + 9nx) = ln(6x + 12)

Reorder the terms:
33n + 9nx = ln(12 + 6x)
33n + 9nx = (12 * ln + 6x * ln)
33n + 9nx = (12ln + 6lnx)

Solving
33n + 9nx = 12ln + 6lnx

Solving for variable 'n'.

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

Add '-12ln' to each side of the equation.
33n + -12ln + 9nx = 12ln + -12ln + 6lnx

Reorder the terms:
-12ln + 33n + 9nx = 12ln + -12ln + 6lnx

Combine like terms: 12ln + -12ln = 0
-12ln + 33n + 9nx = 0 + 6lnx
-12ln + 33n + 9nx = 6lnx

Add '-6lnx' to each side of the equation.
-12ln + 33n + -6lnx + 9nx = 6lnx + -6lnx

Reorder the terms:
-12ln + -6lnx + 33n + 9nx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-12ln + -6lnx + 33n + 9nx = 0

Factor out the Greatest Common Factor (GCF), '3n'.
3n(-4l + -2lx + 11 + 3x) = 0

Ignore the factor 3.

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 '(-4l + -2lx + 11 + 3x)' equal to zero and attempt to solve:

Simplifying
-4l + -2lx + 11 + 3x = 0

Reorder the terms:
11 + -4l + -2lx + 3x = 0

Solving
11 + -4l + -2lx + 3x = 0

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

Add '-11' to each side of the equation.
11 + -4l + -2lx + -11 + 3x = 0 + -11

Reorder the terms:
11 + -11 + -4l + -2lx + 3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4l + -2lx + 3x = 0 + -11
-4l + -2lx + 3x = 0 + -11

Combine like terms: 0 + -11 = -11
-4l + -2lx + 3x = -11

Add '4l' to each side of the equation.
-4l + -2lx + 4l + 3x = -11 + 4l

Reorder the terms:
-4l + 4l + -2lx + 3x = -11 + 4l

Combine like terms: -4l + 4l = 0
0 + -2lx + 3x = -11 + 4l
-2lx + 3x = -11 + 4l

Add '2lx' to each side of the equation.
-2lx + 2lx + 3x = -11 + 4l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 3x = -11 + 4l + 2lx
3x = -11 + 4l + 2lx

Add '-3x' to each side of the equation.
3x + -3x = -11 + 4l + 2lx + -3x

Combine like terms: 3x + -3x = 0
0 = -11 + 4l + 2lx + -3x

Simplifying
0 = -11 + 4l + 2lx + -3x

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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