z^2-23z+112=0

Solution for z^2-23z+112=0 equation:

Simplifying
z2 + -23z + 112 = 0

Reorder the terms:
112 + -23z + z2 = 0

Solving
112 + -23z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + -1z)(16 + -1z) = 0

Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7
Subproblem 2
Set the factor '(16 + -1z)' equal to zero and attempt to solve:

Simplifying
16 + -1z = 0

Solving
16 + -1z = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1z = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1z = 0 + -16
-1z = 0 + -16

Combine like terms: 0 + -16 = -16
-1z = -16

Divide each side by '-1'.
z = 16

Simplifying
z = 16
Solution
z = {7, 16}