2(z+8)z=5

Solution for 2(z+8)z=5 equation:

Simplifying
2(z + 8) * z = 5

Reorder the terms:
2(8 + z) * z = 5

Reorder the terms for easier multiplication:
2z(8 + z) = 5
(8 * 2z + z * 2z) = 5
(16z + 2z2) = 5

Solving
16z + 2z2 = 5

Solving for variable 'z'.

Reorder the terms:
-5 + 16z + 2z2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 16z + 2z2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.5 + 8z + z2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 8z + 2.5 + z2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 8z + z2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 8z + z2 = 0 + 2.5
8z + z2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
8z + z2 = 2.5

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = 2.5 + 16

Reorder the terms:
16 + 8z + z2 = 2.5 + 16

Combine like terms: 2.5 + 16 = 18.5
16 + 8z + z2 = 18.5

Factor a perfect square on the left side:
(z + 4)(z + 4) = 18.5

Calculate the square root of the right side: 4.301162634

Break this problem into two subproblems by setting 
(z + 4) equal to 4.301162634 and -4.301162634.

Subproblem 1
z + 4 = 4.301162634

Simplifying
z + 4 = 4.301162634

Reorder the terms:
4 + z = 4.301162634

Solving
4 + z = 4.301162634

Solving for variable 'z'.

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

Add '-4' to each side of the equation.
4 + -4 + z = 4.301162634 + -4

Combine like terms: 4 + -4 = 0
0 + z = 4.301162634 + -4
z = 4.301162634 + -4

Combine like terms: 4.301162634 + -4 = 0.301162634
z = 0.301162634

Simplifying
z = 0.301162634

Subproblem 2
z + 4 = -4.301162634

Simplifying
z + 4 = -4.301162634

Reorder the terms:
4 + z = -4.301162634

Solving
4 + z = -4.301162634

Solving for variable 'z'.

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

Add '-4' to each side of the equation.
4 + -4 + z = -4.301162634 + -4

Combine like terms: 4 + -4 = 0
0 + z = -4.301162634 + -4
z = -4.301162634 + -4

Combine like terms: -4.301162634 + -4 = -8.301162634
z = -8.301162634

Simplifying
z = -8.301162634

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.301162634, -8.301162634}