z^2=18z-80

Solution for z^2=18z-80 equation:

Simplifying
z2 = 18z + -80

Reorder the terms:
z2 = -80 + 18z

Solving
z2 = -80 + 18z

Solving for variable 'z'.

Reorder the terms:
80 + -18z + z2 = -80 + 18z + 80 + -18z

Reorder the terms:
80 + -18z + z2 = -80 + 80 + 18z + -18z

Combine like terms: -80 + 80 = 0
80 + -18z + z2 = 0 + 18z + -18z
80 + -18z + z2 = 18z + -18z

Combine like terms: 18z + -18z = 0
80 + -18z + z2 = 0

Factor a trinomial.
(8 + -1z)(10 + -1z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1z)' equal to zero and attempt to solve:

Simplifying
10 + -1z = 0

Solving
10 + -1z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1z = 0 + -10
-1z = 0 + -10

Combine like terms: 0 + -10 = -10
-1z = -10

Divide each side by '-1'.
z = 10

Simplifying
z = 10
Solution
z = {8, 10}