z^2-20z=-19

Solution for z^2-20z=-19 equation:

Simplifying
z2 + -20z = -19

Reorder the terms:
-20z + z2 = -19

Solving
-20z + z2 = -19

Solving for variable 'z'.

Reorder the terms:
19 + -20z + z2 = -19 + 19

Combine like terms: -19 + 19 = 0
19 + -20z + z2 = 0

Factor a trinomial.
(1 + -1z)(19 + -1z) = 0

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Subproblem 2
Set the factor '(19 + -1z)' equal to zero and attempt to solve:

Simplifying
19 + -1z = 0

Solving
19 + -1z = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1z = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1z = 0 + -19
-1z = 0 + -19

Combine like terms: 0 + -19 = -19
-1z = -19

Divide each side by '-1'.
z = 19

Simplifying
z = 19
Solution
z = {1, 19}