6x-x^2=2ln(x^2)

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

Simplifying
6x + -1x2 = 2ln(x2)

Multiply ln * x2
6x + -1x2 = 2lnx2

Solving
6x + -1x2 = 2lnx2

Solving for variable 'x'.

Reorder the terms:
-2lnx2 + 6x + -1x2 = 2lnx2 + -2lnx2

Combine like terms: 2lnx2 + -2lnx2 = 0
-2lnx2 + 6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2lnx + 6 + -1x) = 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 '(-2lnx + 6 + -1x)' equal to zero and attempt to solve:

Simplifying
-2lnx + 6 + -1x = 0

Reorder the terms:
6 + -2lnx + -1x = 0

Solving
6 + -2lnx + -1x = 0

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

Add '-6' to each side of the equation.
6 + -2lnx + -6 + -1x = 0 + -6

Reorder the terms:
6 + -6 + -2lnx + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -2lnx + -1x = 0 + -6
-2lnx + -1x = 0 + -6

Combine like terms: 0 + -6 = -6
-2lnx + -1x = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}