(x+5)=(x-1)(x+1)

Solution for (x+5)=(x-1)(x+1) equation:

Simplifying
(x + 5) = (x + -1)(x + 1)

Reorder the terms:
(5 + x) = (x + -1)(x + 1)

Remove parenthesis around (5 + x)
5 + x = (x + -1)(x + 1)

Reorder the terms:
5 + x = (-1 + x)(x + 1)

Reorder the terms:
5 + x = (-1 + x)(1 + x)

Multiply (-1 + x) * (1 + x)
5 + x = (-1(1 + x) + x(1 + x))
5 + x = ((1 * -1 + x * -1) + x(1 + x))
5 + x = ((-1 + -1x) + x(1 + x))
5 + x = (-1 + -1x + (1 * x + x * x))
5 + x = (-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
5 + x = (-1 + 0 + x2)
5 + x = (-1 + x2)

Solving
5 + x = -1 + x2

Solving for variable 'x'.

Reorder the terms:
5 + 1 + x + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: 5 + 1 = 6
6 + x + -1x2 = -1 + x2 + 1 + -1x2

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

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

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

Factor a trinomial.
(3 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x 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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {3, -2}