Z(Z-6)=16

Solution for Z(Z-6)=16 equation:

Simplifying
Z(Z + -6) = 16

Reorder the terms:
Z(-6 + Z) = 16
(-6 * Z + Z * Z) = 16
(-6Z + Z2) = 16

Solving
-6Z + Z2 = 16

Solving for variable 'Z'.

Reorder the terms:
-16 + -6Z + Z2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -6Z + Z2 = 0

Factor a trinomial.
(-2 + -1Z)(8 + -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 '(8 + -1Z)' equal to zero and attempt to solve:

Simplifying
8 + -1Z = 0

Solving
8 + -1Z = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1Z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1Z = 0 + -8
-1Z = 0 + -8

Combine like terms: 0 + -8 = -8
-1Z = -8

Divide each side by '-1'.
Z = 8

Simplifying
Z = 8
Solution
Z = {-2, 8}