12z-36+z^2=0

Solution for 12z-36+z^2=0 equation:

Simplifying
12z + -36 + z2 = 0

Reorder the terms:
-36 + 12z + z2 = 0

Solving
-36 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 12z + 36 + z2 = 0 + 36

Reorder the terms:
-36 + 36 + 12z + z2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 12z + z2 = 0 + 36
12z + z2 = 0 + 36

Combine like terms: 0 + 36 = 36
12z + z2 = 36

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 = 36 + 36

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

Combine like terms: 36 + 36 = 72
36 + 12z + z2 = 72

Factor a perfect square on the left side:
(z + 6)(z + 6) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(z + 6) equal to 8.485281374 and -8.485281374.

Subproblem 1
z + 6 = 8.485281374

Simplifying
z + 6 = 8.485281374

Reorder the terms:
6 + z = 8.485281374

Solving
6 + z = 8.485281374

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 = 8.485281374 + -6

Combine like terms: 6 + -6 = 0
0 + z = 8.485281374 + -6
z = 8.485281374 + -6

Combine like terms: 8.485281374 + -6 = 2.485281374
z = 2.485281374

Simplifying
z = 2.485281374

Subproblem 2
z + 6 = -8.485281374

Simplifying
z + 6 = -8.485281374

Reorder the terms:
6 + z = -8.485281374

Solving
6 + z = -8.485281374

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 = -8.485281374 + -6

Combine like terms: 6 + -6 = 0
0 + z = -8.485281374 + -6
z = -8.485281374 + -6

Combine like terms: -8.485281374 + -6 = -14.485281374
z = -14.485281374

Simplifying
z = -14.485281374

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.485281374, -14.485281374}