x^2+6x+27=22

Solution for x^2+6x+27=22 equation:

Simplifying
x2 + 6x + 27 = 22

Reorder the terms:
27 + 6x + x2 = 22

Solving
27 + 6x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
27 + -22 + 6x + x2 = 22 + -22

Combine like terms: 27 + -22 = 5
5 + 6x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
5 + 6x + x2 = 0

Factor a trinomial.
(5 + x)(1 + x) = 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 '(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 = {-5, -1}