z(z-9)=-20

Solution for z(z-9)=-20 equation:

Simplifying
z(z + -9) = -20

Reorder the terms:
z(-9 + z) = -20
(-9 * z + z * z) = -20
(-9z + z2) = -20

Solving
-9z + z2 = -20

Solving for variable 'z'.

Reorder the terms:
20 + -9z + z2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + -9z + z2 = 0

Factor a trinomial.
(4 + -1z)(5 + -1z) = 0

Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {4, 5}