0=(3x-8)*lnx

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Solution for 0=(3x-8)*lnx equation: 


Simplifying
0 = (3x + -8) * lnx

Reorder the terms:
0 = (-8 + 3x) * lnx

Reorder the terms for easier multiplication:
0 = lnx(-8 + 3x)
0 = (-8 * lnx + 3x * lnx)
0 = (-8lnx + 3lnx2)

Solving
0 = -8lnx + 3lnx2

Solving for variable 'l'.

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

Add '8lnx' to each side of the equation.
0 + 8lnx = -8lnx + 8lnx + 3lnx2
Remove the zero:
8lnx = -8lnx + 8lnx + 3lnx2

Combine like terms: -8lnx + 8lnx = 0
8lnx = 0 + 3lnx2
8lnx = 3lnx2

Add '-3lnx2' to each side of the equation.
8lnx + -3lnx2 = 3lnx2 + -3lnx2

Combine like terms: 3lnx2 + -3lnx2 = 0
8lnx + -3lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(8 + -3x) = 0


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

Simplifying
lnx = 0

Solving
lnx = 0

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

Simplifying
lnx = 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 '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Add '3x' to each side of the equation.
-3x + 3x = -8 + 3x

Combine like terms: -3x + 3x = 0
0 = -8 + 3x

Simplifying
0 = -8 + 3x

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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