x-1=x^2-2x-5

Solution for x-1=x^2-2x-5 equation:

Simplifying
x + -1 = x2 + -2x + -5

Reorder the terms:
-1 + x = x2 + -2x + -5

Reorder the terms:
-1 + x = -5 + -2x + x2

Solving
-1 + x = -5 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + 5 + x + 2x + -1x2 = -5 + -2x + x2 + 5 + 2x + -1x2

Combine like terms: -1 + 5 = 4
4 + x + 2x + -1x2 = -5 + -2x + x2 + 5 + 2x + -1x2

Combine like terms: x + 2x = 3x
4 + 3x + -1x2 = -5 + -2x + x2 + 5 + 2x + -1x2

Reorder the terms:
4 + 3x + -1x2 = -5 + 5 + -2x + 2x + x2 + -1x2

Combine like terms: -5 + 5 = 0
4 + 3x + -1x2 = 0 + -2x + 2x + x2 + -1x2
4 + 3x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
4 + 3x + -1x2 = 0 + x2 + -1x2
4 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(1 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x 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

Simplifying
x = -1
Solution
x = {4, -1}