Ln(x+7)=ln(-4x-8)

Solution for Ln(x+7)=ln(-4x-8) equation:

Simplifying
Ln(x + 7) = ln(-4x + -8)

Reorder the terms:
nL(7 + x) = ln(-4x + -8)
(7 * nL + x * nL) = ln(-4x + -8)
(7nL + nxL) = ln(-4x + -8)

Reorder the terms:
7nL + nxL = ln(-8 + -4x)
7nL + nxL = (-8 * ln + -4x * ln)
7nL + nxL = (-8ln + -4lnx)

Solving
7nL + nxL = -8ln + -4lnx

Solving for variable 'n'.

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

Add '8ln' to each side of the equation.
7nL + 8ln + nxL = -8ln + 8ln + -4lnx

Reorder the terms:
8ln + 7nL + nxL = -8ln + 8ln + -4lnx

Combine like terms: -8ln + 8ln = 0
8ln + 7nL + nxL = 0 + -4lnx
8ln + 7nL + nxL = -4lnx

Add '4lnx' to each side of the equation.
8ln + 7nL + 4lnx + nxL = -4lnx + 4lnx

Reorder the terms:
8ln + 4lnx + 7nL + nxL = -4lnx + 4lnx

Combine like terms: -4lnx + 4lnx = 0
8ln + 4lnx + 7nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(8l + 4lx + 7L + xL) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(8l + 4lx + 7L + xL)' equal to zero and attempt to solve:

Simplifying
8l + 4lx + 7L + xL = 0

Reorder the terms:
7L + 8l + 4lx + xL = 0

Solving
7L + 8l + 4lx + xL = 0

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

Add '-7L' to each side of the equation.
7L + 8l + 4lx + -7L + xL = 0 + -7L

Reorder the terms:
7L + -7L + 8l + 4lx + xL = 0 + -7L

Combine like terms: 7L + -7L = 0
0 + 8l + 4lx + xL = 0 + -7L
8l + 4lx + xL = 0 + -7L
Remove the zero:
8l + 4lx + xL = -7L

Add '-8l' to each side of the equation.
8l + 4lx + -8l + xL = -7L + -8l

Reorder the terms:
8l + -8l + 4lx + xL = -7L + -8l

Combine like terms: 8l + -8l = 0
0 + 4lx + xL = -7L + -8l
4lx + xL = -7L + -8l

Add '-4lx' to each side of the equation.
4lx + -4lx + xL = -7L + -8l + -4lx

Combine like terms: 4lx + -4lx = 0
0 + xL = -7L + -8l + -4lx
xL = -7L + -8l + -4lx

Add '-1xL' to each side of the equation.
xL + -1xL = -7L + -8l + -4lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -7L + -8l + -4lx + -1xL

Simplifying
0 = -7L + -8l + -4lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}