z^2+14z+33=0

Solution for z^2+14z+33=0 equation:

Simplifying
z2 + 14z + 33 = 0

Reorder the terms:
33 + 14z + z2 = 0

Solving
33 + 14z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(11 + z)(3 + 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 '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-11, -3}