4xln(x+6)+32=0

Solution for 4xln(x+6)+32=0 equation:

Simplifying
4xln(x + 6) + 32 = 0

Reorder the terms:
4lnx(6 + x) + 32 = 0
(6 * 4lnx + x * 4lnx) + 32 = 0
(24lnx + 4lnx2) + 32 = 0

Reorder the terms:
32 + 24lnx + 4lnx2 = 0

Solving
32 + 24lnx + 4lnx2 = 0

Solving for variable 'l'.

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

Add '-32' to each side of the equation.
32 + 24lnx + -32 + 4lnx2 = 0 + -32

Reorder the terms:
32 + -32 + 24lnx + 4lnx2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 24lnx + 4lnx2 = 0 + -32
24lnx + 4lnx2 = 0 + -32

Combine like terms: 0 + -32 = -32
24lnx + 4lnx2 = -32

Reorder the terms:
32 + 24lnx + 4lnx2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + 24lnx + 4lnx2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 6lnx + lnx2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(8 + 6lnx + lnx2)' equal to zero and attempt to solve:

Simplifying
8 + 6lnx + lnx2 = 0

Solving
8 + 6lnx + lnx2 = 0

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

Add '-8' to each side of the equation.
8 + 6lnx + -8 + lnx2 = 0 + -8

Reorder the terms:
8 + -8 + 6lnx + lnx2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 6lnx + lnx2 = 0 + -8
6lnx + lnx2 = 0 + -8

Combine like terms: 0 + -8 = -8
6lnx + lnx2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.