x=ln(3x^2)

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

Simplifying
x = ln(3x2)

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

Reorder the terms for easier multiplication:
x = 3ln * x2

Multiply ln * x2
x = 3lnx2

Solving
x = 3lnx2

Solving for variable 'x'.

Reorder the terms:
-3lnx2 + x = 3lnx2 + -3lnx2

Combine like terms: 3lnx2 + -3lnx2 = 0
-3lnx2 + x = 0

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-3lnx + 1)' equal to zero and attempt to solve:

Simplifying
-3lnx + 1 = 0

Reorder the terms:
1 + -3lnx = 0

Solving
1 + -3lnx = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3lnx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3lnx = 0 + -1
-3lnx = 0 + -1

Combine like terms: 0 + -1 = -1
-3lnx = -1

Divide each side by '-3ln'.
x = 0.3333333333l-1n-1

Simplifying
x = 0.3333333333l-1n-1
Solution
x = {0, 0.3333333333l-1n-1}