(logx-1)(3logx-1)=16

Solution for (logx-1)(3logx-1)=16 equation:

Simplifying
(logx + -1)(3logx + -1) = 16

Reorder the terms:
(-1 + glox)(3logx + -1) = 16

Reorder the terms:
(-1 + glox)(-1 + 3glox) = 16

Multiply (-1 + glox) * (-1 + 3glox)
(-1(-1 + 3glox) + glox(-1 + 3glox)) = 16
((-1 * -1 + 3glox * -1) + glox(-1 + 3glox)) = 16
((1 + -3glox) + glox(-1 + 3glox)) = 16
(1 + -3glox + (-1 * glox + 3glox * glox)) = 16
(1 + -3glox + (-1glox + 3g2l2o2x2)) = 16

Combine like terms: -3glox + -1glox = -4glox
(1 + -4glox + 3g2l2o2x2) = 16

Solving
1 + -4glox + 3g2l2o2x2 = 16

Solving for variable 'g'.

Reorder the terms:
1 + -16 + -4glox + 3g2l2o2x2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + -4glox + 3g2l2o2x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + -4glox + 3g2l2o2x2 = 0

Factor a trinomial.
(-5 + -3glox)(3 + -1glox) = 0

Subproblem 1
Set the factor '(-5 + -3glox)' equal to zero and attempt to solve:

Simplifying
-5 + -3glox = 0

Solving
-5 + -3glox = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3glox = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3glox = 0 + 5
-3glox = 0 + 5

Combine like terms: 0 + 5 = 5
-3glox = 5

Divide each side by '-3lox'.
g = -1.666666667l-1o-1x-1

Simplifying
g = -1.666666667l-1o-1x-1
Subproblem 2
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
Solution
g = {-1.666666667l-1o-1x-1, 3l-1o-1x-1}