(z+6)(z+6)=13

Solution for (z+6)(z+6)=13 equation:

Simplifying
(z + 6)(z + 6) = 13

Reorder the terms:
(6 + z)(z + 6) = 13

Reorder the terms:
(6 + z)(6 + z) = 13

Multiply (6 + z) * (6 + z)
(6(6 + z) + z(6 + z)) = 13
((6 * 6 + z * 6) + z(6 + z)) = 13
((36 + 6z) + z(6 + z)) = 13
(36 + 6z + (6 * z + z * z)) = 13
(36 + 6z + (6z + z2)) = 13

Combine like terms: 6z + 6z = 12z
(36 + 12z + z2) = 13

Solving
36 + 12z + z2 = 13

Solving for variable 'z'.

Reorder the terms:
36 + -13 + 12z + z2 = 13 + -13

Combine like terms: 36 + -13 = 23
23 + 12z + z2 = 13 + -13

Combine like terms: 13 + -13 = 0
23 + 12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 12z + -23 + z2 = 0 + -23

Reorder the terms:
23 + -23 + 12z + z2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 12z + z2 = 0 + -23
12z + z2 = 0 + -23

Combine like terms: 0 + -23 = -23
12z + z2 = -23

The z term is 12z.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12z + 36 + z2 = -23 + 36

Reorder the terms:
36 + 12z + z2 = -23 + 36

Combine like terms: -23 + 36 = 13
36 + 12z + z2 = 13

Factor a perfect square on the left side:
(z + 6)(z + 6) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(z + 6) equal to 3.605551275 and -3.605551275.

Subproblem 1
z + 6 = 3.605551275

Simplifying
z + 6 = 3.605551275

Reorder the terms:
6 + z = 3.605551275

Solving
6 + z = 3.605551275

Solving for variable 'z'.

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

Add '-6' to each side of the equation.
6 + -6 + z = 3.605551275 + -6

Combine like terms: 6 + -6 = 0
0 + z = 3.605551275 + -6
z = 3.605551275 + -6

Combine like terms: 3.605551275 + -6 = -2.394448725
z = -2.394448725

Simplifying
z = -2.394448725

Subproblem 2
z + 6 = -3.605551275

Simplifying
z + 6 = -3.605551275

Reorder the terms:
6 + z = -3.605551275

Solving
6 + z = -3.605551275

Solving for variable 'z'.

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

Add '-6' to each side of the equation.
6 + -6 + z = -3.605551275 + -6

Combine like terms: 6 + -6 = 0
0 + z = -3.605551275 + -6
z = -3.605551275 + -6

Combine like terms: -3.605551275 + -6 = -9.605551275
z = -9.605551275

Simplifying
z = -9.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-2.394448725, -9.605551275}