logx*logx-6logx=27

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

Simplifying
logx * logx + -6logx = 27

Multiply glox * glox
g2l2o2x2 + -6logx = 27

Reorder the terms:
-6glox + g2l2o2x2 = 27

Solving
-6glox + g2l2o2x2 = 27

Solving for variable 'g'.

Reorder the terms:
-27 + -6glox + g2l2o2x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -6glox + g2l2o2x2 = 0

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

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

Simplifying
-3 + -1glox = 0

Solving
-3 + -1glox = 0

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

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

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

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

Divide each side by '-1lox'.
g = -3l-1o-1x-1

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

Simplifying
9 + -1glox = 0

Solving
9 + -1glox = 0

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

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

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

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

Divide each side by '-1lox'.
g = 9l-1o-1x-1

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