3xln(x+6)+2x=0

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Solution for 3xln(x+6)+2x=0 equation: 


Simplifying
3xln(x + 6) + 2x = 0

Reorder the terms:
3lnx(6 + x) + 2x = 0
(6 * 3lnx + x * 3lnx) + 2x = 0
(18lnx + 3lnx2) + 2x = 0

Solving
18lnx + 3lnx2 + 2x = 0

Solving for variable 'l'.

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

Add '-2x' to each side of the equation.
18lnx + 3lnx2 + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
18lnx + 3lnx2 + 0 = 0 + -2x
18lnx + 3lnx2 = 0 + -2x
Remove the zero:
18lnx + 3lnx2 = -2x

Combine like terms: -2x + 2x = 0
18lnx + 3lnx2 + 2x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(18ln + 3lnx + 2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

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 '(18ln + 3lnx + 2)' equal to zero and attempt to solve:

Simplifying
18ln + 3lnx + 2 = 0

Reorder the terms:
2 + 18ln + 3lnx = 0

Solving
2 + 18ln + 3lnx = 0

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

Add '-2' to each side of the equation.
2 + 18ln + -2 + 3lnx = 0 + -2

Reorder the terms:
2 + -2 + 18ln + 3lnx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 18ln + 3lnx = 0 + -2
18ln + 3lnx = 0 + -2

Combine like terms: 0 + -2 = -2
18ln + 3lnx = -2

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.

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