F(x)=x^2-8ln(x)

Solution for F(x)=x^2-8ln(x) equation:

Simplifying
F(x) = x2 + -8ln(x)

Multiply F * x
xF = x2 + -8ln(x)

Multiply ln * x
xF = x2 + -8lnx

Reorder the terms:
xF = -8lnx + x2

Solving
xF = -8lnx + x2

Solving for variable 'x'.

Reorder the terms:
8lnx + xF + -1x2 = -8lnx + x2 + 8lnx + -1x2

Reorder the terms:
8lnx + xF + -1x2 = -8lnx + 8lnx + x2 + -1x2

Combine like terms: -8lnx + 8lnx = 0
8lnx + xF + -1x2 = 0 + x2 + -1x2
8lnx + xF + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8lnx + xF + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8ln + F + -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 '(8ln + F + -1x)' equal to zero and attempt to solve:

Simplifying
8ln + F + -1x = 0

Reorder the terms:
F + 8ln + -1x = 0

Solving
F + 8ln + -1x = 0

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

Add '-1F' to each side of the equation.
F + 8ln + -1F + -1x = 0 + -1F

Reorder the terms:
F + -1F + 8ln + -1x = 0 + -1F

Combine like terms: F + -1F = 0
0 + 8ln + -1x = 0 + -1F
8ln + -1x = 0 + -1F
Remove the zero:
8ln + -1x = -1F

Add '-8ln' to each side of the equation.
8ln + -8ln + -1x = -1F + -8ln

Combine like terms: 8ln + -8ln = 0
0 + -1x = -1F + -8ln
-1x = -1F + -8ln

Divide each side by '-1'.
x = F + 8ln

Simplifying
x = F + 8ln
Solution
x = {0, F + 8ln}