4xln(x)*(ln(x)+1)=0

Solution for 4xln(x)*(ln(x)+1)=0 equation:

Simplifying
4xln(x)(ln(x) + 1) = 0

Multiply ln * x
4lnx * x(lnx + 1) = 0

Reorder the terms:
4lnx * x(1 + lnx) = 0

Multiply lnx * x
4lnx2(1 + lnx) = 0
(1 * 4lnx2 + lnx * 4lnx2) = 0
(4lnx2 + 4l2n2x3) = 0

Solving
4lnx2 + 4l2n2x3 = 0

Solving for variable 'l'.

Factor out the Greatest Common Factor (GCF), '4lnx2'.
4lnx2(1 + lnx) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'lnx2' equal to zero and attempt to solve:

Simplifying
lnx2 = 0

Solving
lnx2 = 0

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

Simplifying
lnx2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + lnx)' equal to zero and attempt to solve:

Simplifying
1 + lnx = 0

Solving
1 + lnx = 0

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

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

Combine like terms: 1 + -1 = 0
0 + lnx = 0 + -1
lnx = 0 + -1

Combine like terms: 0 + -1 = -1
lnx = -1

Divide each side by 'nx'.
l = -1n-1x-1

Simplifying
l = -1n-1x-1
Solution
l = {-1n-1x-1}