log(3)(x-3)+log(3)(x-5)=2

Solution for log(3)(x-3)+log(3)(x-5)=2 equation:

Simplifying
log(3)(x + -3) + log(3)(x + -5) = 2

Reorder the terms:
glo * 3(-3 + x) + log(3)(x + -5) = 2

Reorder the terms for easier multiplication:
3glo(-3 + x) + log(3)(x + -5) = 2
(-3 * 3glo + x * 3glo) + log(3)(x + -5) = 2
(-9glo + 3glox) + log(3)(x + -5) = 2

Reorder the terms:
-9glo + 3glox + glo * 3(-5 + x) = 2

Reorder the terms for easier multiplication:
-9glo + 3glox + 3glo(-5 + x) = 2
-9glo + 3glox + (-5 * 3glo + x * 3glo) = 2
-9glo + 3glox + (-15glo + 3glox) = 2

Reorder the terms:
-9glo + -15glo + 3glox + 3glox = 2

Combine like terms: -9glo + -15glo = -24glo
-24glo + 3glox + 3glox = 2

Combine like terms: 3glox + 3glox = 6glox
-24glo + 6glox = 2

Solving
-24glo + 6glox = 2

Solving for variable 'g'.

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

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

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

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

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

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

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

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

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

Combine like terms: 0 + 1 = 1
-12glo + 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.