ln(x^2+12)=ln(-9x-2)

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Solution for ln(x^2+12)=ln(-9x-2) equation: 


Simplifying
ln(x2 + 12) = ln(-9x + -2)

Reorder the terms:
ln(12 + x2) = ln(-9x + -2)
(12 * ln + x2 * ln) = ln(-9x + -2)
(12ln + lnx2) = ln(-9x + -2)

Reorder the terms:
12ln + lnx2 = ln(-2 + -9x)
12ln + lnx2 = (-2 * ln + -9x * ln)
12ln + lnx2 = (-2ln + -9lnx)

Solving
12ln + lnx2 = -2ln + -9lnx

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
12ln + 2ln + lnx2 = -2ln + 2ln + -9lnx

Combine like terms: 12ln + 2ln = 14ln
14ln + lnx2 = -2ln + 2ln + -9lnx

Combine like terms: -2ln + 2ln = 0
14ln + lnx2 = 0 + -9lnx
14ln + lnx2 = -9lnx

Add '9lnx' to each side of the equation.
14ln + 9lnx + lnx2 = -9lnx + 9lnx

Combine like terms: -9lnx + 9lnx = 0
14ln + 9lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(14 + 9x + x2) = 0

Factor a trinomial.
ln((7 + x)(2 + x)) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 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 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

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

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

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

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

Simplifying
0 = -7 + -1x

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 l 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.

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