z^2+20=8z+5

Solution for z^2+20=8z+5 equation:

Simplifying
z2 + 20 = 8z + 5

Reorder the terms:
20 + z2 = 8z + 5

Reorder the terms:
20 + z2 = 5 + 8z

Solving
20 + z2 = 5 + 8z

Solving for variable 'z'.

Reorder the terms:
20 + -5 + -8z + z2 = 5 + 8z + -5 + -8z

Combine like terms: 20 + -5 = 15
15 + -8z + z2 = 5 + 8z + -5 + -8z

Reorder the terms:
15 + -8z + z2 = 5 + -5 + 8z + -8z

Combine like terms: 5 + -5 = 0
15 + -8z + z2 = 0 + 8z + -8z
15 + -8z + z2 = 8z + -8z

Combine like terms: 8z + -8z = 0
15 + -8z + z2 = 0

Factor a trinomial.
(3 + -1z)(5 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
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 = {3, 5}