F(x)=ln(x)*x^2

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

Simplifying
F(x) = ln(x) * x2

Multiply F * x
xF = ln(x) * x2

Multiply ln * x
xF = lnx * x2

Multiply lnx * x2
xF = lnx3

Solving
xF = lnx3

Solving for variable 'x'.

Reorder the terms:
-1lnx3 + xF = lnx3 + -1lnx3

Combine like terms: lnx3 + -1lnx3 = 0
-1lnx3 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1lnx2 + 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 '(-1lnx2 + F)' equal to zero and attempt to solve:

Simplifying
-1lnx2 + F = 0

Reorder the terms:
F + -1lnx2 = 0

Solving
F + -1lnx2 = 0

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

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

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

Divide each side by '-1ln'.
x2 = l-1n-1F

Simplifying
x2 = l-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}