(z+12)z=(4+8)4

Solution for (z+12)z=(4+8)4 equation:

Simplifying
(z + 12) * z = (4 + 8) * 4

Reorder the terms:
(12 + z) * z = (4 + 8) * 4

Reorder the terms for easier multiplication:
z(12 + z) = (4 + 8) * 4
(12 * z + z * z) = (4 + 8) * 4
(12z + z2) = (4 + 8) * 4

Combine like terms: 4 + 8 = 12
12z + z2 = (12) * 4

Multiply 12 * 4
12z + z2 = 48

Solving
12z + z2 = 48

Solving for variable 'z'.

Reorder the terms:
-48 + 12z + z2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 12z + 48 + z2 = 0 + 48

Reorder the terms:
-48 + 48 + 12z + z2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 12z + z2 = 0 + 48
12z + z2 = 0 + 48

Combine like terms: 0 + 48 = 48
12z + z2 = 48

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 = 48 + 36

Reorder the terms:
36 + 12z + z2 = 48 + 36

Combine like terms: 48 + 36 = 84
36 + 12z + z2 = 84

Factor a perfect square on the left side:
(z + 6)(z + 6) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(z + 6) equal to 9.16515139 and -9.16515139.

Subproblem 1
z + 6 = 9.16515139

Simplifying
z + 6 = 9.16515139

Reorder the terms:
6 + z = 9.16515139

Solving
6 + z = 9.16515139

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 = 9.16515139 + -6

Combine like terms: 6 + -6 = 0
0 + z = 9.16515139 + -6
z = 9.16515139 + -6

Combine like terms: 9.16515139 + -6 = 3.16515139
z = 3.16515139

Simplifying
z = 3.16515139

Subproblem 2
z + 6 = -9.16515139

Simplifying
z + 6 = -9.16515139

Reorder the terms:
6 + z = -9.16515139

Solving
6 + z = -9.16515139

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 = -9.16515139 + -6

Combine like terms: 6 + -6 = 0
0 + z = -9.16515139 + -6
z = -9.16515139 + -6

Combine like terms: -9.16515139 + -6 = -15.16515139
z = -15.16515139

Simplifying
z = -15.16515139

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.16515139, -15.16515139}