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.
(-8 + -1Z)(2 + -1Z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
Z = {-8, 2}