z^2+13z+22=0

Solution for z^2+13z+22=0 equation:

Simplifying
z2 + 13z + 22 = 0

Reorder the terms:
22 + 13z + z2 = 0

Solving
22 + 13z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(11 + z)(2 + z) = 0

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

Simplifying
11 + z = 0

Solving
11 + z = 0

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

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

Combine like terms: 11 + -11 = 0
0 + z = 0 + -11
z = 0 + -11

Combine like terms: 0 + -11 = -11
z = -11

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

Simplifying
2 + z = 0

Solving
2 + z = 0

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

Add '-2' to each side of the equation.
2 + -2 + z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

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