ln(2x+1)ln(x-2)-2lnx=0

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Solution for ln(2x+1)ln(x-2)-2lnx=0 equation: 


Simplifying
ln(2x + 1) * ln(x + -2) + -2lnx = 0

Reorder the terms:
ln(1 + 2x) * ln(x + -2) + -2lnx = 0

Reorder the terms:
ln(1 + 2x) * ln(-2 + x) + -2lnx = 0

Reorder the terms for easier multiplication:
ln * ln(1 + 2x)(-2 + x) + -2lnx = 0

Multiply ln * ln
l2n2(1 + 2x)(-2 + x) + -2lnx = 0

Multiply (1 + 2x) * (-2 + x)
l2n2(1(-2 + x) + 2x * (-2 + x)) + -2lnx = 0
l2n2((-2 * 1 + x * 1) + 2x * (-2 + x)) + -2lnx = 0
l2n2((-2 + 1x) + 2x * (-2 + x)) + -2lnx = 0
l2n2(-2 + 1x + (-2 * 2x + x * 2x)) + -2lnx = 0
l2n2(-2 + 1x + (-4x + 2x2)) + -2lnx = 0

Combine like terms: 1x + -4x = -3x
l2n2(-2 + -3x + 2x2) + -2lnx = 0
(-2 * l2n2 + -3x * l2n2 + 2x2 * l2n2) + -2lnx = 0
(-2l2n2 + -3l2n2x + 2l2n2x2) + -2lnx = 0

Reorder the terms:
-2lnx + -2l2n2 + -3l2n2x + 2l2n2x2 = 0

Solving
-2lnx + -2l2n2 + -3l2n2x + 2l2n2x2 = 0

Solving for variable 'l'.

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2x + -2ln + -3lnx + 2lnx2) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 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 '(-2x + -2ln + -3lnx + 2lnx2)' equal to zero and attempt to solve:

Simplifying
-2x + -2ln + -3lnx + 2lnx2 = 0

Reorder the terms:
-2ln + -3lnx + 2lnx2 + -2x = 0

Solving
-2ln + -3lnx + 2lnx2 + -2x = 0

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

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

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

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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