8=6z-z^2

Solution for 8=6z-z^2 equation:

Simplifying
8 = 6z + -1z2

Solving
8 = 6z + -1z2

Solving for variable 'z'.

Reorder the terms:
8 + -6z + z2 = 6z + -6z + -1z2 + z2

Combine like terms: 6z + -6z = 0
8 + -6z + z2 = 0 + -1z2 + z2
8 + -6z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
8 + -6z + z2 = 0

Factor a trinomial.
(2 + -1z)(4 + -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 '(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
Solution
z = {2, 4}