(2lnx-1)lnx=1

Solution for (2lnx-1)lnx=1 equation:

Simplifying
(2lnx + -1) * lnx = 1

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

Reorder the terms for easier multiplication:
lnx(-1 + 2lnx) = 1
(-1 * lnx + 2lnx * lnx) = 1
(-1lnx + 2l2n2x2) = 1

Solving
-1lnx + 2l2n2x2 = 1

Solving for variable 'l'.

Reorder the terms:
-1 + -1lnx + 2l2n2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -1lnx + 2l2n2x2 = 0

Factor a trinomial.
(-1 + -2lnx)(1 + -1lnx) = 0

Subproblem 1
Set the factor '(-1 + -2lnx)' equal to zero and attempt to solve:

Simplifying
-1 + -2lnx = 0

Solving
-1 + -2lnx = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -2lnx = 0 + 1
-2lnx = 0 + 1

Combine like terms: 0 + 1 = 1
-2lnx = 1

Divide each side by '-2nx'.
l = -0.5n-1x-1

Simplifying
l = -0.5n-1x-1
Subproblem 2
Set the factor '(1 + -1lnx)' equal to zero and attempt to solve:

Simplifying
1 + -1lnx = 0

Solving
1 + -1lnx = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1lnx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1lnx = 0 + -1
-1lnx = 0 + -1

Combine like terms: 0 + -1 = -1
-1lnx = -1

Divide each side by '-1nx'.
l = n-1x-1

Simplifying
l = n-1x-1
Solution
l = {-0.5n-1x-1, n-1x-1}