8x-22=x^2-x-2

Solution for 8x-22=x^2-x-2 equation:

Simplifying
8x + -22 = x2 + -1x + -2

Reorder the terms:
-22 + 8x = x2 + -1x + -2

Reorder the terms:
-22 + 8x = -2 + -1x + x2

Solving
-22 + 8x = -2 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-22 + 2 + 8x + x + -1x2 = -2 + -1x + x2 + 2 + x + -1x2

Combine like terms: -22 + 2 = -20
-20 + 8x + x + -1x2 = -2 + -1x + x2 + 2 + x + -1x2

Combine like terms: 8x + x = 9x
-20 + 9x + -1x2 = -2 + -1x + x2 + 2 + x + -1x2

Reorder the terms:
-20 + 9x + -1x2 = -2 + 2 + -1x + x + x2 + -1x2

Combine like terms: -2 + 2 = 0
-20 + 9x + -1x2 = 0 + -1x + x + x2 + -1x2
-20 + 9x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-20 + 9x + -1x2 = 0 + x2 + -1x2
-20 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + 9x + -1x2 = 0

Factor a trinomial.
(-5 + x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
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
Solution
x = {5, 4}