ln((x+3)(x-8))-ln(x+3)=ln(3)

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Solution for ln((x+3)(x-8))-ln(x+3)=ln(3) equation: 


Simplifying
ln((x + 3)(x + -8)) + -1ln(x + 3) = ln(3)

Reorder the terms:
ln((3 + x)(x + -8)) + -1ln(x + 3) = ln(3)

Reorder the terms:
ln((3 + x)(-8 + x)) + -1ln(x + 3) = ln(3)

Multiply (3 + x) * (-8 + x)
ln((3(-8 + x) + x(-8 + x))) + -1ln(x + 3) = ln(3)
ln(((-8 * 3 + x * 3) + x(-8 + x))) + -1ln(x + 3) = ln(3)
ln(((-24 + 3x) + x(-8 + x))) + -1ln(x + 3) = ln(3)
ln((-24 + 3x + (-8 * x + x * x))) + -1ln(x + 3) = ln(3)
ln((-24 + 3x + (-8x + x2))) + -1ln(x + 3) = ln(3)

Combine like terms: 3x + -8x = -5x
ln((-24 + -5x + x2)) + -1ln(x + 3) = ln(3)
(-24 * ln + -5x * ln + x2 * ln) + -1ln(x + 3) = ln(3)
(-24ln + -5lnx + lnx2) + -1ln(x + 3) = ln(3)

Reorder the terms:
-24ln + -5lnx + lnx2 + -1ln(3 + x) = ln(3)
-24ln + -5lnx + lnx2 + (3 * -1ln + x * -1ln) = ln(3)
-24ln + -5lnx + lnx2 + (-3ln + -1lnx) = ln(3)

Reorder the terms:
-24ln + -3ln + -5lnx + -1lnx + lnx2 = ln(3)

Combine like terms: -24ln + -3ln = -27ln
-27ln + -5lnx + -1lnx + lnx2 = ln(3)

Combine like terms: -5lnx + -1lnx = -6lnx
-27ln + -6lnx + lnx2 = ln(3)

Reorder the terms for easier multiplication:
-27ln + -6lnx + lnx2 = 3ln

Solving
-27ln + -6lnx + lnx2 = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-27ln + -6lnx + -3ln + lnx2 = 3ln + -3ln

Reorder the terms:
-27ln + -3ln + -6lnx + lnx2 = 3ln + -3ln

Combine like terms: -27ln + -3ln = -30ln
-30ln + -6lnx + lnx2 = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-30ln + -6lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-30 + -6x + x2) = 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 '(-30 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + -6x + x2 = 0

Solving
-30 + -6x + x2 = 0

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

Add '30' to each side of the equation.
-30 + -6x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -6x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -6x + x2 = 0 + 30
-6x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-6x + x2 = 30

Add '6x' to each side of the equation.
-6x + 6x + x2 = 30 + 6x

Combine like terms: -6x + 6x = 0
0 + x2 = 30 + 6x
x2 = 30 + 6x

Add '-1x2' to each side of the equation.
x2 + -1x2 = 30 + 6x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 30 + 6x + -1x2

Simplifying
0 = 30 + 6x + -1x2

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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