lnx*lnx-6lnx=27

Solution for lnx*lnx-6lnx=27 equation:

Simplifying
lnx * lnx + -6lnx = 27

Multiply lnx * lnx
l2n2x2 + -6lnx = 27

Reorder the terms:
-6lnx + l2n2x2 = 27

Solving
-6lnx + l2n2x2 = 27

Solving for variable 'l'.

Reorder the terms:
-27 + -6lnx + l2n2x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -6lnx + l2n2x2 = 0

Factor a trinomial.
(-3 + -1lnx)(9 + -1lnx) = 0

Subproblem 1
Set the factor '(-3 + -1lnx)' equal to zero and attempt to solve:

Simplifying
-3 + -1lnx = 0

Solving
-3 + -1lnx = 0

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

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

Combine like terms: -3 + 3 = 0
0 + -1lnx = 0 + 3
-1lnx = 0 + 3

Combine like terms: 0 + 3 = 3
-1lnx = 3

Divide each side by '-1nx'.
l = -3n-1x-1

Simplifying
l = -3n-1x-1
Subproblem 2
Set the factor '(9 + -1lnx)' equal to zero and attempt to solve:

Simplifying
9 + -1lnx = 0

Solving
9 + -1lnx = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1lnx = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1lnx = 0 + -9
-1lnx = 0 + -9

Combine like terms: 0 + -9 = -9
-1lnx = -9

Divide each side by '-1nx'.
l = 9n-1x-1

Simplifying
l = 9n-1x-1
Solution
l = {-3n-1x-1, 9n-1x-1}