Ln(x-6)(x+1)=ln(x-15)

Solution for Ln(x-6)(x+1)=ln(x-15) equation:

Simplifying
Ln(x + -6)(x + 1) = ln(x + -15)

Reorder the terms:
nL(-6 + x)(x + 1) = ln(x + -15)

Reorder the terms:
nL(-6 + x)(1 + x) = ln(x + -15)

Multiply (-6 + x) * (1 + x)
nL(-6(1 + x) + x(1 + x)) = ln(x + -15)
nL((1 * -6 + x * -6) + x(1 + x)) = ln(x + -15)
nL((-6 + -6x) + x(1 + x)) = ln(x + -15)
nL(-6 + -6x + (1 * x + x * x)) = ln(x + -15)
nL(-6 + -6x + (1x + x2)) = ln(x + -15)

Combine like terms: -6x + 1x = -5x
nL(-6 + -5x + x2) = ln(x + -15)
(-6 * nL + -5x * nL + x2 * nL) = ln(x + -15)
(-6nL + -5nxL + nx2L) = ln(x + -15)

Reorder the terms:
-6nL + -5nxL + nx2L = ln(-15 + x)
-6nL + -5nxL + nx2L = (-15 * ln + x * ln)
-6nL + -5nxL + nx2L = (-15ln + lnx)

Solving
-6nL + -5nxL + nx2L = -15ln + lnx

Solving for variable 'n'.

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

Add '15ln' to each side of the equation.
-6nL + -5nxL + 15ln + nx2L = -15ln + 15ln + lnx

Reorder the terms:
15ln + -6nL + -5nxL + nx2L = -15ln + 15ln + lnx

Combine like terms: -15ln + 15ln = 0
15ln + -6nL + -5nxL + nx2L = 0 + lnx
15ln + -6nL + -5nxL + nx2L = lnx

Add '-1lnx' to each side of the equation.
15ln + -6nL + -5nxL + -1lnx + nx2L = lnx + -1lnx

Reorder the terms:
15ln + -1lnx + -6nL + -5nxL + nx2L = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
15ln + -1lnx + -6nL + -5nxL + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(15l + -1lx + -6L + -5xL + x2L) = 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 '(15l + -1lx + -6L + -5xL + x2L)' equal to zero and attempt to solve:

Simplifying
15l + -1lx + -6L + -5xL + x2L = 0

Reorder the terms:
-6L + 15l + -1lx + -5xL + x2L = 0

Solving
-6L + 15l + -1lx + -5xL + x2L = 0

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

Add '6L' to each side of the equation.
-6L + 15l + -1lx + -5xL + 6L + x2L = 0 + 6L

Reorder the terms:
-6L + 6L + 15l + -1lx + -5xL + x2L = 0 + 6L

Combine like terms: -6L + 6L = 0
0 + 15l + -1lx + -5xL + x2L = 0 + 6L
15l + -1lx + -5xL + x2L = 0 + 6L
Remove the zero:
15l + -1lx + -5xL + x2L = 6L

Add '-15l' to each side of the equation.
15l + -1lx + -5xL + -15l + x2L = 6L + -15l

Reorder the terms:
15l + -15l + -1lx + -5xL + x2L = 6L + -15l

Combine like terms: 15l + -15l = 0
0 + -1lx + -5xL + x2L = 6L + -15l
-1lx + -5xL + x2L = 6L + -15l

Add 'lx' to each side of the equation.
-1lx + -5xL + lx + x2L = 6L + -15l + lx

Reorder the terms:
-1lx + lx + -5xL + x2L = 6L + -15l + lx

Combine like terms: -1lx + lx = 0
0 + -5xL + x2L = 6L + -15l + lx
-5xL + x2L = 6L + -15l + lx

Add '5xL' to each side of the equation.
-5xL + 5xL + x2L = 6L + -15l + lx + 5xL

Combine like terms: -5xL + 5xL = 0
0 + x2L = 6L + -15l + lx + 5xL
x2L = 6L + -15l + lx + 5xL

Add '-1x2L' to each side of the equation.
x2L + -1x2L = 6L + -15l + lx + 5xL + -1x2L

Combine like terms: x2L + -1x2L = 0
0 = 6L + -15l + lx + 5xL + -1x2L

Simplifying
0 = 6L + -15l + lx + 5xL + -1x2L

The solution to this equation could not be determined.

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