ln(x-2)+ln(x+10)=ln(x^2+8x-20)

Solution for ln(x-2)+ln(x+10)=ln(x^2+8x-20) equation:

Simplifying
ln(x + -2) + ln(x + 10) = ln(x2 + 8x + -20)

Reorder the terms:
ln(-2 + x) + ln(x + 10) = ln(x2 + 8x + -20)
(-2 * ln + x * ln) + ln(x + 10) = ln(x2 + 8x + -20)
(-2ln + lnx) + ln(x + 10) = ln(x2 + 8x + -20)

Reorder the terms:
-2ln + lnx + ln(10 + x) = ln(x2 + 8x + -20)
-2ln + lnx + (10 * ln + x * ln) = ln(x2 + 8x + -20)
-2ln + lnx + (10ln + lnx) = ln(x2 + 8x + -20)

Reorder the terms:
-2ln + 10ln + lnx + lnx = ln(x2 + 8x + -20)

Combine like terms: -2ln + 10ln = 8ln
8ln + lnx + lnx = ln(x2 + 8x + -20)

Combine like terms: lnx + lnx = 2lnx
8ln + 2lnx = ln(x2 + 8x + -20)

Reorder the terms:
8ln + 2lnx = ln(-20 + 8x + x2)
8ln + 2lnx = (-20 * ln + 8x * ln + x2 * ln)
8ln + 2lnx = (-20ln + 8lnx + lnx2)

Solving
8ln + 2lnx = -20ln + 8lnx + lnx2

Solving for variable 'l'.

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

Add '20ln' to each side of the equation.
8ln + 20ln + 2lnx = -20ln + 8lnx + 20ln + lnx2

Combine like terms: 8ln + 20ln = 28ln
28ln + 2lnx = -20ln + 8lnx + 20ln + lnx2

Reorder the terms:
28ln + 2lnx = -20ln + 20ln + 8lnx + lnx2

Combine like terms: -20ln + 20ln = 0
28ln + 2lnx = 0 + 8lnx + lnx2
28ln + 2lnx = 8lnx + lnx2

Add '-8lnx' to each side of the equation.
28ln + 2lnx + -8lnx = 8lnx + -8lnx + lnx2

Combine like terms: 2lnx + -8lnx = -6lnx
28ln + -6lnx = 8lnx + -8lnx + lnx2

Combine like terms: 8lnx + -8lnx = 0
28ln + -6lnx = 0 + lnx2
28ln + -6lnx = lnx2

Add '-1lnx2' to each side of the equation.
28ln + -6lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
28ln + -6lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(28 + -6x + -1x2) = 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 '(28 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
28 + -6x + -1x2 = 0

Solving
28 + -6x + -1x2 = 0

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

Add '-28' to each side of the equation.
28 + -6x + -28 + -1x2 = 0 + -28

Reorder the terms:
28 + -28 + -6x + -1x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -6x + -1x2 = 0 + -28
-6x + -1x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-6x + -1x2 = -28

Add '6x' to each side of the equation.
-6x + 6x + -1x2 = -28 + 6x

Combine like terms: -6x + 6x = 0
0 + -1x2 = -28 + 6x
-1x2 = -28 + 6x

Add 'x2' to each side of the equation.
-1x2 + x2 = -28 + 6x + x2

Combine like terms: -1x2 + x2 = 0
0 = -28 + 6x + x2

Simplifying
0 = -28 + 6x + x2

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.