What is the solution to the equation below? log6 4x 2 - log6 x=2

Log[6] * 4x2 + -1log[6] * x = 2

Reorder the terms for easier multiplication:
6 * 4glo * x2 + -1log[6] * x = 2

Multiply 6 * 4
24glo * x2 + -1log[6] * x = 2

Multiply glo * x2
24glox2 + -1log[6] * x = 2

Reorder the terms for easier multiplication:
24glox2 + -1 * 6glo * x = 2

Multiply -1 * 6
24glox2 + -6glo * x = 2

Multiply glo * x
24glox2 + -6glox = 2

Reorder the terms:
-6glox + 24glox2 = 2

Solving
-6glox + 24glox2 = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -6glox + 24glox2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -6glox + 24glox2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3glox + 12glox2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3glox + 12glox2)' equal to zero and attempt to solve:

Simplifying
-1 + -3glox + 12glox2 = 0

Solving
-1 + -3glox + 12glox2 = 0

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

Add '1' to each side of the equation.
-1 + -3glox + 1 + 12glox2 = 0 + 1

Reorder the terms:
-1 + 1 + -3glox + 12glox2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3glox + 12glox2 = 0 + 1
-3glox + 12glox2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3glox + 12glox2 = 1