log(x+3)+log(x+4)=log(x^3+12x^2)-log(x)

Solution for log(x+3)+log(x+4)=log(x^3+12x^2)-log(x) equation:

Simplifying
log(x + 3) + log(x + 4) = log(x3 + 12x2) + -1log(x)

Reorder the terms:
glo(3 + x) + log(x + 4) = log(x3 + 12x2) + -1log(x)
(3 * glo + x * glo) + log(x + 4) = log(x3 + 12x2) + -1log(x)
(3glo + glox) + log(x + 4) = log(x3 + 12x2) + -1log(x)

Reorder the terms:
3glo + glox + glo(4 + x) = log(x3 + 12x2) + -1log(x)
3glo + glox + (4 * glo + x * glo) = log(x3 + 12x2) + -1log(x)
3glo + glox + (4glo + glox) = log(x3 + 12x2) + -1log(x)

Reorder the terms:
3glo + 4glo + glox + glox = log(x3 + 12x2) + -1log(x)

Combine like terms: 3glo + 4glo = 7glo
7glo + glox + glox = log(x3 + 12x2) + -1log(x)

Combine like terms: glox + glox = 2glox
7glo + 2glox = log(x3 + 12x2) + -1log(x)

Reorder the terms:
7glo + 2glox = glo(12x2 + x3) + -1log(x)
7glo + 2glox = (12x2 * glo + x3 * glo) + -1log(x)
7glo + 2glox = (12glox2 + glox3) + -1log(x)

Multiply glo * x
7glo + 2glox = 12glox2 + glox3 + -1glox

Reorder the terms:
7glo + 2glox = -1glox + 12glox2 + glox3

Solving
7glo + 2glox = -1glox + 12glox2 + glox3

Solving for variable 'g'.

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

Add 'glox' to each side of the equation.
7glo + 2glox + glox = -1glox + 12glox2 + glox + glox3

Combine like terms: 2glox + glox = 3glox
7glo + 3glox = -1glox + 12glox2 + glox + glox3

Reorder the terms:
7glo + 3glox = -1glox + glox + 12glox2 + glox3

Combine like terms: -1glox + glox = 0
7glo + 3glox = 0 + 12glox2 + glox3
7glo + 3glox = 12glox2 + glox3

Add '-12glox2' to each side of the equation.
7glo + 3glox + -12glox2 = 12glox2 + -12glox2 + glox3

Combine like terms: 12glox2 + -12glox2 = 0
7glo + 3glox + -12glox2 = 0 + glox3
7glo + 3glox + -12glox2 = glox3

Add '-1glox3' to each side of the equation.
7glo + 3glox + -12glox2 + -1glox3 = glox3 + -1glox3

Combine like terms: glox3 + -1glox3 = 0
7glo + 3glox + -12glox2 + -1glox3 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(7 + 3x + -12x2 + -1x3) = 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 + 3x + -12x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
7 + 3x + -12x2 + -1x3 = 0

Solving
7 + 3x + -12x2 + -1x3 = 0

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

Add '-7' to each side of the equation.
7 + 3x + -12x2 + -7 + -1x3 = 0 + -7

Reorder the terms:
7 + -7 + 3x + -12x2 + -1x3 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x + -12x2 + -1x3 = 0 + -7
3x + -12x2 + -1x3 = 0 + -7

Combine like terms: 0 + -7 = -7
3x + -12x2 + -1x3 = -7

Add '-3x' to each side of the equation.
3x + -12x2 + -3x + -1x3 = -7 + -3x

Reorder the terms:
3x + -3x + -12x2 + -1x3 = -7 + -3x

Combine like terms: 3x + -3x = 0
0 + -12x2 + -1x3 = -7 + -3x
-12x2 + -1x3 = -7 + -3x

Add '12x2' to each side of the equation.
-12x2 + 12x2 + -1x3 = -7 + -3x + 12x2

Combine like terms: -12x2 + 12x2 = 0
0 + -1x3 = -7 + -3x + 12x2
-1x3 = -7 + -3x + 12x2

Add 'x3' to each side of the equation.
-1x3 + x3 = -7 + -3x + 12x2 + x3

Combine like terms: -1x3 + x3 = 0
0 = -7 + -3x + 12x2 + x3

Simplifying
0 = -7 + -3x + 12x2 + x3

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.