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

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


Simplifying
x = x(ln3x + -3ln2x + 6lnx + -6)

Reorder the terms:
x = x(-6 + 6lnx + -3ln2x + ln3x)
x = (-6 * x + 6lnx * x + -3ln2x * x + ln3x * x)

Reorder the terms:
x = (6lnx2 + -3ln2x2 + ln3x2 + -6x)
x = (6lnx2 + -3ln2x2 + ln3x2 + -6x)

Solving
x = 6lnx2 + -3ln2x2 + ln3x2 + -6x

Solving for variable 'x'.

Reorder the terms:
-6lnx2 + 3ln2x2 + -1ln3x2 + x + 6x = 6lnx2 + -3ln2x2 + ln3x2 + -6x + -6lnx2 + 3ln2x2 + -1ln3x2 + 6x

Combine like terms: x + 6x = 7x
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = 6lnx2 + -3ln2x2 + ln3x2 + -6x + -6lnx2 + 3ln2x2 + -1ln3x2 + 6x

Reorder the terms:
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = 6lnx2 + -6lnx2 + -3ln2x2 + 3ln2x2 + ln3x2 + -1ln3x2 + -6x + 6x

Combine like terms: 6lnx2 + -6lnx2 = 0
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = 0 + -3ln2x2 + 3ln2x2 + ln3x2 + -1ln3x2 + -6x + 6x
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = -3ln2x2 + 3ln2x2 + ln3x2 + -1ln3x2 + -6x + 6x

Combine like terms: -3ln2x2 + 3ln2x2 = 0
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = 0 + ln3x2 + -1ln3x2 + -6x + 6x
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = ln3x2 + -1ln3x2 + -6x + 6x

Combine like terms: ln3x2 + -1ln3x2 = 0
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = 0 + -6x + 6x
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = -6x + 6x

Combine like terms: -6x + 6x = 0
-6lnx2 + 3ln2x2 + -1ln3x2 + 7x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6lnx + 3ln2x + -1ln3x + 7) = 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 '(-6lnx + 3ln2x + -1ln3x + 7)' equal to zero and attempt to solve:

Simplifying
-6lnx + 3ln2x + -1ln3x + 7 = 0

Reorder the terms:
7 + -6lnx + 3ln2x + -1ln3x = 0

Solving
7 + -6lnx + 3ln2x + -1ln3x = 0

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

Add '-7' to each side of the equation.
7 + -6lnx + 3ln2x + -7 + -1ln3x = 0 + -7

Reorder the terms:
7 + -7 + -6lnx + 3ln2x + -1ln3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6lnx + 3ln2x + -1ln3x = 0 + -7
-6lnx + 3ln2x + -1ln3x = 0 + -7

Combine like terms: 0 + -7 = -7
-6lnx + 3ln2x + -1ln3x = -7

The solution to this equation could not be determined.

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

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