z(z-1)=20

Solution for z(z-1)=20 equation:

Simplifying
z(z + -1) = 20

Reorder the terms:
z(-1 + z) = 20
(-1 * z + z * z) = 20
(-1z + z2) = 20

Solving
-1z + z2 = 20

Solving for variable 'z'.

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

Combine like terms: 20 + -20 = 0
-20 + -1z + 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}