ln(x^3+x^2-2)=ln[(x-1)*(x^2-1)]

Solution for ln(x^3+x^2-2)=ln[(x-1)*(x^2-1)] equation:

Simplifying
ln(x3 + x2 + -2) = ln[(x + -1)(x2 + -1)]

Reorder the terms:
ln(-2 + x2 + x3) = ln[(x + -1)(x2 + -1)]
(-2 * ln + x2 * ln + x3 * ln) = ln[(x + -1)(x2 + -1)]
(-2ln + lnx2 + lnx3) = ln[(x + -1)(x2 + -1)]

Reorder the terms:
-2ln + lnx2 + lnx3 = ln[(-1 + x)(x2 + -1)]

Reorder the terms:
-2ln + lnx2 + lnx3 = ln[(-1 + x)(-1 + x2)]

Multiply (-1 + x) * (-1 + x2)
-2ln + lnx2 + lnx3 = ln[(-1(-1 + x2) + x(-1 + x2))]
-2ln + lnx2 + lnx3 = ln[((-1 * -1 + x2 * -1) + x(-1 + x2))]
-2ln + lnx2 + lnx3 = ln[((1 + -1x2) + x(-1 + x2))]
-2ln + lnx2 + lnx3 = ln[(1 + -1x2 + (-1 * x + x2 * x))]
-2ln + lnx2 + lnx3 = ln[(1 + -1x2 + (-1x + x3))]

Reorder the terms:
-2ln + lnx2 + lnx3 = ln[(1 + -1x + -1x2 + x3)]
-2ln + lnx2 + lnx3 = ln[(1 + -1x + -1x2 + x3)]
-2ln + lnx2 + lnx3 = [1 * ln + -1x * ln + -1x2 * ln + x3 * ln]
-2ln + lnx2 + lnx3 = [1ln + -1lnx + -1lnx2 + lnx3]

Add '-1lnx3' to each side of the equation.
-2ln + lnx2 + lnx3 + -1lnx3 = 1ln + -1lnx + -1lnx2 + lnx3 + -1lnx3

Combine like terms: lnx3 + -1lnx3 = 0
-2ln + lnx2 + 0 = 1ln + -1lnx + -1lnx2 + lnx3 + -1lnx3
-2ln + lnx2 = 1ln + -1lnx + -1lnx2 + lnx3 + -1lnx3

Combine like terms: lnx3 + -1lnx3 = 0
-2ln + lnx2 = 1ln + -1lnx + -1lnx2 + 0
-2ln + lnx2 = 1ln + -1lnx + -1lnx2

Solving
-2ln + lnx2 = 1ln + -1lnx + -1lnx2

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-2ln + -1ln + lnx2 = 1ln + -1lnx + -1ln + -1lnx2

Combine like terms: -2ln + -1ln = -3ln
-3ln + lnx2 = 1ln + -1lnx + -1ln + -1lnx2

Reorder the terms:
-3ln + lnx2 = 1ln + -1ln + -1lnx + -1lnx2

Combine like terms: 1ln + -1ln = 0
-3ln + lnx2 = 0 + -1lnx + -1lnx2
-3ln + lnx2 = -1lnx + -1lnx2

Add 'lnx' to each side of the equation.
-3ln + lnx + lnx2 = -1lnx + lnx + -1lnx2

Combine like terms: -1lnx + lnx = 0
-3ln + lnx + lnx2 = 0 + -1lnx2
-3ln + lnx + lnx2 = -1lnx2

Add 'lnx2' to each side of the equation.
-3ln + lnx + lnx2 + lnx2 = -1lnx2 + lnx2

Combine like terms: lnx2 + lnx2 = 2lnx2
-3ln + lnx + 2lnx2 = -1lnx2 + lnx2

Combine like terms: -1lnx2 + lnx2 = 0
-3ln + lnx + 2lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + x + 2x2) = 0

Factor a trinomial.
ln((-3 + -2x)(1 + -1x)) = 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 '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Add '2x' to each side of the equation.
-2x + 2x = 3 + 2x

Combine like terms: -2x + 2x = 0
0 = 3 + 2x

Simplifying
0 = 3 + 2x

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
0 = -1 + x

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.