z^2-8z=20

Solution for z^2-8z=20 equation:

Simplifying
z2 + -8z = 20

Reorder the terms:
-8z + z2 = 20

Solving
-8z + z2 = 20

Solving for variable 'z'.

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

Combine like terms: 20 + -20 = 0
-20 + -8z + z2 = 0

Factor a trinomial.
(-2 + -1z)(10 + -1z) = 0

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(10 + -1z)' equal to zero and attempt to solve:

Simplifying
10 + -1z = 0

Solving
10 + -1z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1z = 0 + -10
-1z = 0 + -10

Combine like terms: 0 + -10 = -10
-1z = -10

Divide each side by '-1'.
z = 10

Simplifying
z = 10
Solution
z = {-2, 10}