F(x)=9xln(3x)-9x

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Solution for F(x)=9xln(3x)-9x equation: 


Simplifying
F(x) = 9xln(3x) + -9x

Multiply F * x
xF = 9xln(3x) + -9x

Remove parenthesis around (3x)
xF = 9lnx * 3x + -9x

Reorder the terms for easier multiplication:
xF = 9 * 3lnx * x + -9x

Multiply 9 * 3
xF = 27lnx * x + -9x

Multiply lnx * x
xF = 27lnx2 + -9x

Solving
xF = 27lnx2 + -9x

Solving for variable 'x'.

Reorder the terms:
-27lnx2 + 9x + xF = 27lnx2 + -9x + -27lnx2 + 9x

Reorder the terms:
-27lnx2 + 9x + xF = 27lnx2 + -27lnx2 + -9x + 9x

Combine like terms: 27lnx2 + -27lnx2 = 0
-27lnx2 + 9x + xF = 0 + -9x + 9x
-27lnx2 + 9x + xF = -9x + 9x

Combine like terms: -9x + 9x = 0
-27lnx2 + 9x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27lnx + 9 + 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 '(-27lnx + 9 + F)' equal to zero and attempt to solve:

Simplifying
-27lnx + 9 + F = 0

Reorder the terms:
9 + F + -27lnx = 0

Solving
9 + F + -27lnx = 0

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

Add '-9' to each side of the equation.
9 + F + -9 + -27lnx = 0 + -9

Reorder the terms:
9 + -9 + F + -27lnx = 0 + -9

Combine like terms: 9 + -9 = 0
0 + F + -27lnx = 0 + -9
F + -27lnx = 0 + -9

Combine like terms: 0 + -9 = -9
F + -27lnx = -9

Add '-1F' to each side of the equation.
F + -1F + -27lnx = -9 + -1F

Combine like terms: F + -1F = 0
0 + -27lnx = -9 + -1F
-27lnx = -9 + -1F

Divide each side by '-27ln'.
x = 0.3333333333l-1n-1 + 0.03703703704l-1n-1F

Simplifying
x = 0.3333333333l-1n-1 + 0.03703703704l-1n-1F
Solution
x = {0, 0.3333333333l-1n-1 + 0.03703703704l-1n-1F}

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