x^2+8x=22-x

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

Simplifying
x2 + 8x = 22 + -1x

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

Solving
8x + x2 = 22 + -1x

Solving for variable 'x'.

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

Combine like terms: 8x + x = 9x
-22 + 9x + x2 = 22 + -1x + -22 + x

Reorder the terms:
-22 + 9x + x2 = 22 + -22 + -1x + x

Combine like terms: 22 + -22 = 0
-22 + 9x + x2 = 0 + -1x + x
-22 + 9x + x2 = -1x + x

Combine like terms: -1x + x = 0
-22 + 9x + x2 = 0

Factor a trinomial.
(-11 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-11, 2}