z^2-11z+19=-5

Solution for z^2-11z+19=-5 equation:

Simplifying
z2 + -11z + 19 = -5

Reorder the terms:
19 + -11z + z2 = -5

Solving
19 + -11z + z2 = -5

Solving for variable 'z'.

Reorder the terms:
19 + 5 + -11z + z2 = -5 + 5

Combine like terms: 19 + 5 = 24
24 + -11z + z2 = -5 + 5

Combine like terms: -5 + 5 = 0
24 + -11z + z2 = 0

Factor a trinomial.
(3 + -1z)(8 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 0

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

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

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

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

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

Simplifying
z = 8
Solution
z = {3, 8}