F(x)=x-(2lnx)

Solution for F(x)=x-(2lnx) equation:

Simplifying
F(x) = x + -1(2lnx)

Multiply F * x
xF = x + -1(2lnx)

Remove parenthesis around (2lnx)
xF = x + -1 * 2lnx

Multiply -1 * 2
xF = x + -2lnx

Reorder the terms:
xF = -2lnx + x

Solving
xF = -2lnx + x

Solving for variable 'x'.

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

Add '2lnx' to each side of the equation.
2lnx + xF = -2lnx + 2lnx + x

Combine like terms: -2lnx + 2lnx = 0
2lnx + xF = 0 + x
2lnx + xF = x

Add '-1x' to each side of the equation.
2lnx + -1x + xF = x + -1x

Combine like terms: x + -1x = 0
2lnx + -1x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2ln + -1 + 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 '(2ln + -1 + F)' equal to zero and attempt to solve:

Simplifying
2ln + -1 + F = 0

Reorder the terms:
-1 + F + 2ln = 0

Solving
-1 + F + 2ln = 0

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

Add '1' to each side of the equation.
-1 + F + 1 + 2ln = 0 + 1

Reorder the terms:
-1 + 1 + F + 2ln = 0 + 1

Combine like terms: -1 + 1 = 0
0 + F + 2ln = 0 + 1
F + 2ln = 0 + 1

Combine like terms: 0 + 1 = 1
F + 2ln = 1

Add '-1F' to each side of the equation.
F + -1F + 2ln = 1 + -1F

Combine like terms: F + -1F = 0
0 + 2ln = 1 + -1F
2ln = 1 + -1F

Add '-2ln' to each side of the equation.
2ln + -2ln = 1 + -1F + -2ln

Combine like terms: 2ln + -2ln = 0
0 = 1 + -1F + -2ln

Simplifying
0 = 1 + -1F + -2ln

The solution to this equation could not be determined.

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