0=z^2-9z+20

Solution for 0=z^2-9z+20 equation:

Simplifying
0 = z2 + -9z + 20

Reorder the terms:
0 = 20 + -9z + z2

Solving
0 = 20 + -9z + z2

Solving for variable 'z'.

Combine like terms: 0 + -20 = -20
-20 + 9z + -1z2 = 20 + -9z + z2 + -20 + 9z + -1z2

Reorder the terms:
-20 + 9z + -1z2 = 20 + -20 + -9z + 9z + z2 + -1z2

Combine like terms: 20 + -20 = 0
-20 + 9z + -1z2 = 0 + -9z + 9z + z2 + -1z2
-20 + 9z + -1z2 = -9z + 9z + z2 + -1z2

Combine like terms: -9z + 9z = 0
-20 + 9z + -1z2 = 0 + z2 + -1z2
-20 + 9z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-20 + 9z + -1z2 = 0

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

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

Simplifying
-5 + z = 0

Solving
-5 + z = 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 + z = 0 + 5

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

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

Simplifying
z = 5
Subproblem 2
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
Solution
z = {5, 4}