log(x+10)-log^2=log(3x+3)

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Solution for log(x+10)-log^2=log(3x+3) equation: 


Simplifying
log(x + 10) + -1log2 = log(3x + 3)

Reorder the terms:
glo(10 + x) + -1log2 = log(3x + 3)
(10 * glo + x * glo) + -1log2 = log(3x + 3)
(10glo + glox) + -1log2 = log(3x + 3)

Reorder the terms:
10glo + glox + -1g2lo = glo(3 + 3x)
10glo + glox + -1g2lo = (3 * glo + 3x * glo)
10glo + glox + -1g2lo = (3glo + 3glox)

Solving
10glo + glox + -1g2lo = 3glo + 3glox

Solving for variable 'g'.

Reorder the terms:
10glo + -3glo + glox + -3glox + -1g2lo = 3glo + 3glox + -3glo + -3glox

Combine like terms: 10glo + -3glo = 7glo
7glo + glox + -3glox + -1g2lo = 3glo + 3glox + -3glo + -3glox

Combine like terms: glox + -3glox = -2glox
7glo + -2glox + -1g2lo = 3glo + 3glox + -3glo + -3glox

Reorder the terms:
7glo + -2glox + -1g2lo = 3glo + -3glo + 3glox + -3glox

Combine like terms: 3glo + -3glo = 0
7glo + -2glox + -1g2lo = 0 + 3glox + -3glox
7glo + -2glox + -1g2lo = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
7glo + -2glox + -1g2lo = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(7 + -2x + -1g) = 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 '(7 + -2x + -1g)' equal to zero and attempt to solve:

Simplifying
7 + -2x + -1g = 0

Reorder the terms:
7 + -1g + -2x = 0

Solving
7 + -1g + -2x = 0

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

Add '-7' to each side of the equation.
7 + -1g + -7 + -2x = 0 + -7

Reorder the terms:
7 + -7 + -1g + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1g + -2x = 0 + -7
-1g + -2x = 0 + -7

Combine like terms: 0 + -7 = -7
-1g + -2x = -7

Add '2x' to each side of the equation.
-1g + -2x + 2x = -7 + 2x

Combine like terms: -2x + 2x = 0
-1g + 0 = -7 + 2x
-1g = -7 + 2x

Divide each side by '-1'.
g = 7 + -2x

Simplifying
g = 7 + -2x
Solution
g = {7 + -2x}

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