[x+1]=x^2-5

Solution for [x+1]=x^2-5 equation:

Simplifying
[x + 1] = x2 + -5

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

Remove brackets around [1 + x]
1 + x = x2 + -5

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

Solving
1 + x = -5 + x2

Solving for variable 'x'.

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

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

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

Combine like terms: -5 + 5 = 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}