log[5](x-3)+log[5](x+21)=2

Solution for log[5](x-3)+log[5](x+21)=2 equation:

Simplifying
log[5](x + -3) + log[5](x + 21) = 2

Reorder the terms:
glo * 5(-3 + x) + log[5](x + 21) = 2

Reorder the terms for easier multiplication:
5glo(-3 + x) + log[5](x + 21) = 2
(-3 * 5glo + x * 5glo) + log[5](x + 21) = 2
(-15glo + 5glox) + log[5](x + 21) = 2

Reorder the terms:
-15glo + 5glox + glo * 5(21 + x) = 2

Reorder the terms for easier multiplication:
-15glo + 5glox + 5glo(21 + x) = 2
-15glo + 5glox + (21 * 5glo + x * 5glo) = 2
-15glo + 5glox + (105glo + 5glox) = 2

Reorder the terms:
-15glo + 105glo + 5glox + 5glox = 2

Combine like terms: -15glo + 105glo = 90glo
90glo + 5glox + 5glox = 2

Combine like terms: 5glox + 5glox = 10glox
90glo + 10glox = 2

Solving
90glo + 10glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + 90glo + 10glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 90glo + 10glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 45glo + 5glox) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 45glo + 5glox)' equal to zero and attempt to solve:

Simplifying
-1 + 45glo + 5glox = 0

Solving
-1 + 45glo + 5glox = 0

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

Add '1' to each side of the equation.
-1 + 45glo + 1 + 5glox = 0 + 1

Reorder the terms:
-1 + 1 + 45glo + 5glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 45glo + 5glox = 0 + 1
45glo + 5glox = 0 + 1

Combine like terms: 0 + 1 = 1
45glo + 5glox = 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.