z^2-20=22-z

Solution for z^2-20=22-z equation:

Simplifying
z2 + -20 = 22 + -1z

Reorder the terms:
-20 + z2 = 22 + -1z

Solving
-20 + z2 = 22 + -1z

Solving for variable 'z'.

Reorder the terms:
-20 + -22 + z + z2 = 22 + -1z + -22 + z

Combine like terms: -20 + -22 = -42
-42 + z + z2 = 22 + -1z + -22 + z

Reorder the terms:
-42 + z + z2 = 22 + -22 + -1z + z

Combine like terms: 22 + -22 = 0
-42 + z + z2 = 0 + -1z + z
-42 + z + z2 = -1z + z

Combine like terms: -1z + z = 0
-42 + z + z2 = 0

Factor a trinomial.
(-7 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-7, 6}