F(x)=3xln(6x)-3x

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Solution for F(x)=3xln(6x)-3x equation: 


Simplifying
F(x) = 3xln(6x) + -3x

Multiply F * x
xF = 3xln(6x) + -3x

Remove parenthesis around (6x)
xF = 3lnx * 6x + -3x

Reorder the terms for easier multiplication:
xF = 3 * 6lnx * x + -3x

Multiply 3 * 6
xF = 18lnx * x + -3x

Multiply lnx * x
xF = 18lnx2 + -3x

Solving
xF = 18lnx2 + -3x

Solving for variable 'x'.

Reorder the terms:
-18lnx2 + 3x + xF = 18lnx2 + -3x + -18lnx2 + 3x

Reorder the terms:
-18lnx2 + 3x + xF = 18lnx2 + -18lnx2 + -3x + 3x

Combine like terms: 18lnx2 + -18lnx2 = 0
-18lnx2 + 3x + xF = 0 + -3x + 3x
-18lnx2 + 3x + xF = -3x + 3x

Combine like terms: -3x + 3x = 0
-18lnx2 + 3x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18lnx + 3 + F) = 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 '(-18lnx + 3 + F)' equal to zero and attempt to solve:

Simplifying
-18lnx + 3 + F = 0

Reorder the terms:
3 + F + -18lnx = 0

Solving
3 + F + -18lnx = 0

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

Add '-3' to each side of the equation.
3 + F + -3 + -18lnx = 0 + -3

Reorder the terms:
3 + -3 + F + -18lnx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + F + -18lnx = 0 + -3
F + -18lnx = 0 + -3

Combine like terms: 0 + -3 = -3
F + -18lnx = -3

Add '-1F' to each side of the equation.
F + -1F + -18lnx = -3 + -1F

Combine like terms: F + -1F = 0
0 + -18lnx = -3 + -1F
-18lnx = -3 + -1F

Divide each side by '-18ln'.
x = 0.1666666667l-1n-1 + 0.05555555556l-1n-1F

Simplifying
x = 0.1666666667l-1n-1 + 0.05555555556l-1n-1F
Solution
x = {0, 0.1666666667l-1n-1 + 0.05555555556l-1n-1F}

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