ln(3-x)*(x+1)=0

Solution for ln(3-x)*(x+1)=0 equation:

Simplifying
ln(3 + -1x)(x + 1) = 0

Reorder the terms:
ln(3 + -1x)(1 + x) = 0

Multiply (3 + -1x) * (1 + x)
ln(3(1 + x) + -1x * (1 + x)) = 0
ln((1 * 3 + x * 3) + -1x * (1 + x)) = 0
ln((3 + 3x) + -1x * (1 + x)) = 0
ln(3 + 3x + (1 * -1x + x * -1x)) = 0
ln(3 + 3x + (-1x + -1x2)) = 0

Combine like terms: 3x + -1x = 2x
ln(3 + 2x + -1x2) = 0
(3 * ln + 2x * ln + -1x2 * ln) = 0
(3ln + 2lnx + -1lnx2) = 0

Solving
3ln + 2lnx + -1lnx2 = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + 2x + -1x2) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Add 'x' to each side of the equation.
-1x + x = -3 + x

Combine like terms: -1x + x = 0
0 = -3 + x

Simplifying
0 = -3 + x

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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -1x

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.