(3x^2)+ln(6x)=ln(3)

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Solution for (3x^2)+ln(6x)=ln(3) equation: 


Simplifying
(3x2) + ln(6x) = ln(3)

Remove parenthesis around (6x)
(3x2) + ln * 6x = ln(3)

Reorder the terms for easier multiplication:
(3x2) + 6ln * x = ln(3)

Multiply ln * x
(3x2) + 6lnx = ln(3)

Reorder the terms:
6lnx + (3x2) = ln(3)

Reorder the terms for easier multiplication:
6lnx + (3x2) = 3ln

Solving
6lnx + (3x2) = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
6lnx + -3ln + (3x2) = 3ln + -3ln

Reorder the terms:
-3ln + 6lnx + (3x2) = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-3ln + 6lnx + (3x2) = 0

Add '(-3x2)' to each side of the equation.
-3ln + 6lnx + (3x2) + (-3x2) = 0 + (-3x2)

Combine like terms: (3x2) + (-3x2) = 0
-3ln + 6lnx + 0 = 0 + (-3x2)
-3ln + 6lnx = 0 + (-3x2)
Remove the zero:
-3ln + 6lnx = (-3x2)

Combine like terms: (-3x2) + (3x2) = 0
-3ln + 6lnx + (3x2) = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1ln + 2lnx + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1ln + 2lnx + x2)' equal to zero and attempt to solve:

Simplifying
-1ln + 2lnx + x2 = 0

Solving
-1ln + 2lnx + x2 = 0

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

Add '-1x2' to each side of the equation.
-1ln + 2lnx + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-1ln + 2lnx + 0 = 0 + -1x2
-1ln + 2lnx = 0 + -1x2
Remove the zero:
-1ln + 2lnx = -1x2

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.

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