log(x+1)+log(x+5)=log(x^2+2x+1)-log(x+1)

Solution for log(x+1)+log(x+5)=log(x^2+2x+1)-log(x+1) equation:

Simplifying
log(x + 1) + log(x + 5) = log(x2 + 2x + 1) + -1log(x + 1)

Reorder the terms:
glo(1 + x) + log(x + 5) = log(x2 + 2x + 1) + -1log(x + 1)
(1 * glo + x * glo) + log(x + 5) = log(x2 + 2x + 1) + -1log(x + 1)
(1glo + glox) + log(x + 5) = log(x2 + 2x + 1) + -1log(x + 1)

Reorder the terms:
1glo + glox + glo(5 + x) = log(x2 + 2x + 1) + -1log(x + 1)
1glo + glox + (5 * glo + x * glo) = log(x2 + 2x + 1) + -1log(x + 1)
1glo + glox + (5glo + glox) = log(x2 + 2x + 1) + -1log(x + 1)

Reorder the terms:
1glo + 5glo + glox + glox = log(x2 + 2x + 1) + -1log(x + 1)

Combine like terms: 1glo + 5glo = 6glo
6glo + glox + glox = log(x2 + 2x + 1) + -1log(x + 1)

Combine like terms: glox + glox = 2glox
6glo + 2glox = log(x2 + 2x + 1) + -1log(x + 1)

Reorder the terms:
6glo + 2glox = glo(1 + 2x + x2) + -1log(x + 1)
6glo + 2glox = (1 * glo + 2x * glo + x2 * glo) + -1log(x + 1)
6glo + 2glox = (1glo + 2glox + glox2) + -1log(x + 1)

Reorder the terms:
6glo + 2glox = 1glo + 2glox + glox2 + -1glo(1 + x)
6glo + 2glox = 1glo + 2glox + glox2 + (1 * -1glo + x * -1glo)
6glo + 2glox = 1glo + 2glox + glox2 + (-1glo + -1glox)

Reorder the terms:
6glo + 2glox = 1glo + -1glo + 2glox + -1glox + glox2

Combine like terms: 1glo + -1glo = 0
6glo + 2glox = 0 + 2glox + -1glox + glox2
6glo + 2glox = 2glox + -1glox + glox2

Combine like terms: 2glox + -1glox = 1glox
6glo + 2glox = 1glox + glox2

Solving
6glo + 2glox = 1glox + glox2

Solving for variable 'g'.

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

Add '-1glox' to each side of the equation.
6glo + 2glox + -1glox = 1glox + -1glox + glox2

Combine like terms: 2glox + -1glox = 1glox
6glo + 1glox = 1glox + -1glox + glox2

Combine like terms: 1glox + -1glox = 0
6glo + 1glox = 0 + glox2
6glo + 1glox = glox2

Add '-1glox2' to each side of the equation.
6glo + 1glox + -1glox2 = glox2 + -1glox2

Combine like terms: glox2 + -1glox2 = 0
6glo + 1glox + -1glox2 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(6 + x + -1x2) = 0

Factor a trinomial.
glo((3 + -1x)(2 + x)) = 0

Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve:

Simplifying
glo = 0

Solving
glo = 0

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

Simplifying
glo = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Add 'x' to each side of the equation.
-1x + x = -3 + x

Combine like terms: -1x + x = 0
0 = -3 + x

Simplifying
0 = -3 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

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.