x*x+6x+6=22

Solution for x*x+6x+6=22 equation:

Simplifying
x * x + 6x + 6 = 22

Multiply x * x
x2 + 6x + 6 = 22

Reorder the terms:
6 + 6x + x2 = 22

Solving
6 + 6x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
6 + -22 + 6x + x2 = 22 + -22

Combine like terms: 6 + -22 = -16
-16 + 6x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-16 + 6x + x2 = 0

Factor a trinomial.
(-8 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 2}