log(6)(x-3)-log(6)(2x-1)=2

Solution for log(6)(x-3)-log(6)(2x-1)=2 equation:

Simplifying
log(6)(x + -3) + -1log(6)(2x + -1) = 2

Reorder the terms:
glo * 6(-3 + x) + -1log(6)(2x + -1) = 2

Reorder the terms for easier multiplication:
6glo(-3 + x) + -1log(6)(2x + -1) = 2
(-3 * 6glo + x * 6glo) + -1log(6)(2x + -1) = 2
(-18glo + 6glox) + -1log(6)(2x + -1) = 2

Reorder the terms:
-18glo + 6glox + -1glo * 6(-1 + 2x) = 2

Reorder the terms for easier multiplication:
-18glo + 6glox + -1 * 6glo(-1 + 2x) = 2

Multiply -1 * 6
-18glo + 6glox + -6glo(-1 + 2x) = 2
-18glo + 6glox + (-1 * -6glo + 2x * -6glo) = 2
-18glo + 6glox + (6glo + -12glox) = 2

Reorder the terms:
-18glo + 6glo + 6glox + -12glox = 2

Combine like terms: -18glo + 6glo = -12glo
-12glo + 6glox + -12glox = 2

Combine like terms: 6glox + -12glox = -6glox
-12glo + -6glox = 2

Solving
-12glo + -6glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -12glo + -6glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -12glo + -6glox = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 6glo + 3glox) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 6glo + 3glox)' equal to zero and attempt to solve:

Simplifying
1 + 6glo + 3glox = 0

Solving
1 + 6glo + 3glox = 0

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

Add '-1' to each side of the equation.
1 + 6glo + -1 + 3glox = 0 + -1

Reorder the terms:
1 + -1 + 6glo + 3glox = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6glo + 3glox = 0 + -1
6glo + 3glox = 0 + -1

Combine like terms: 0 + -1 = -1
6glo + 3glox = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.