F(x)=ln(24x-4x^3)

Solution for F(x)=ln(24x-4x^3) equation:

Simplifying
F(x) = ln(24x + -4x3)

Multiply F * x
xF = ln(24x + -4x3)
xF = (24x * ln + -4x3 * ln)
xF = (24lnx + -4lnx3)

Solving
xF = 24lnx + -4lnx3

Solving for variable 'x'.

Reorder the terms:
-24lnx + 4lnx3 + xF = 24lnx + -4lnx3 + -24lnx + 4lnx3

Reorder the terms:
-24lnx + 4lnx3 + xF = 24lnx + -24lnx + -4lnx3 + 4lnx3

Combine like terms: 24lnx + -24lnx = 0
-24lnx + 4lnx3 + xF = 0 + -4lnx3 + 4lnx3
-24lnx + 4lnx3 + xF = -4lnx3 + 4lnx3

Combine like terms: -4lnx3 + 4lnx3 = 0
-24lnx + 4lnx3 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24ln + 4lnx2 + 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 '(-24ln + 4lnx2 + F)' equal to zero and attempt to solve:

Simplifying
-24ln + 4lnx2 + F = 0

Reorder the terms:
F + -24ln + 4lnx2 = 0

Solving
F + -24ln + 4lnx2 = 0

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

Add '-1F' to each side of the equation.
F + -24ln + -1F + 4lnx2 = 0 + -1F

Reorder the terms:
F + -1F + -24ln + 4lnx2 = 0 + -1F

Combine like terms: F + -1F = 0
0 + -24ln + 4lnx2 = 0 + -1F
-24ln + 4lnx2 = 0 + -1F
Remove the zero:
-24ln + 4lnx2 = -1F

Add '24ln' to each side of the equation.
-24ln + 24ln + 4lnx2 = -1F + 24ln

Combine like terms: -24ln + 24ln = 0
0 + 4lnx2 = -1F + 24ln
4lnx2 = -1F + 24ln

Divide each side by '4ln'.
x2 = -0.25l-1n-1F + 6

Simplifying
x2 = -0.25l-1n-1F + 6

Reorder the terms:
x2 = 6 + -0.25l-1n-1F

The solution to this equation could not be determined.

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