ln*x-ln*x^2+ln*x-3x^3=0

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Solution for ln*x-ln*x^2+ln*x-3x^3=0 equation: 


Simplifying
ln * x + -1ln * x2 + ln * x + -3x3 = 0

Multiply ln * x
lnx + -1ln * x2 + ln * x + -3x3 = 0

Multiply ln * x2
lnx + -1lnx2 + ln * x + -3x3 = 0

Multiply ln * x
lnx + -1lnx2 + lnx + -3x3 = 0

Reorder the terms:
lnx + lnx + -1lnx2 + -3x3 = 0

Combine like terms: lnx + lnx = 2lnx
2lnx + -1lnx2 + -3x3 = 0

Solving
2lnx + -1lnx2 + -3x3 = 0

Solving for variable 'l'.

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

Add '3x3' to each side of the equation.
2lnx + -1lnx2 + -3x3 + 3x3 = 0 + 3x3

Combine like terms: -3x3 + 3x3 = 0
2lnx + -1lnx2 + 0 = 0 + 3x3
2lnx + -1lnx2 = 0 + 3x3
Remove the zero:
2lnx + -1lnx2 = 3x3

Combine like terms: 3x3 + -3x3 = 0
2lnx + -1lnx2 + -3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2ln + -1lnx + -3x2) = 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 '(2ln + -1lnx + -3x2)' equal to zero and attempt to solve:

Simplifying
2ln + -1lnx + -3x2 = 0

Solving
2ln + -1lnx + -3x2 = 0

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

Add '3x2' to each side of the equation.
2ln + -1lnx + -3x2 + 3x2 = 0 + 3x2

Combine like terms: -3x2 + 3x2 = 0
2ln + -1lnx + 0 = 0 + 3x2
2ln + -1lnx = 0 + 3x2
Remove the zero:
2ln + -1lnx = 3x2

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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