x+(x+2)=x^2-22

Solution for x+(x+2)=x^2-22 equation:

Simplifying
x + (x + 2) = x2 + -22

Reorder the terms:
x + (2 + x) = x2 + -22

Remove parenthesis around (2 + x)
x + 2 + x = x2 + -22

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

Combine like terms: x + x = 2x
2 + 2x = x2 + -22

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

Solving
2 + 2x = -22 + x2

Solving for variable 'x'.

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

Combine like terms: 2 + 22 = 24
24 + 2x + -1x2 = -22 + x2 + 22 + -1x2

Reorder the terms:
24 + 2x + -1x2 = -22 + 22 + x2 + -1x2

Combine like terms: -22 + 22 = 0
24 + 2x + -1x2 = 0 + x2 + -1x2
24 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 2x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(4 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {6, -4}