z^2+35+12z-1=180

Solution for z^2+35+12z-1=180 equation:

Simplifying
z2 + 35 + 12z + -1 = 180

Reorder the terms:
35 + -1 + 12z + z2 = 180

Combine like terms: 35 + -1 = 34
34 + 12z + z2 = 180

Solving
34 + 12z + z2 = 180

Solving for variable 'z'.

Reorder the terms:
34 + -180 + 12z + z2 = 180 + -180

Combine like terms: 34 + -180 = -146
-146 + 12z + z2 = 180 + -180

Combine like terms: 180 + -180 = 0
-146 + 12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '146' to each side of the equation.
-146 + 12z + 146 + z2 = 0 + 146

Reorder the terms:
-146 + 146 + 12z + z2 = 0 + 146

Combine like terms: -146 + 146 = 0
0 + 12z + z2 = 0 + 146
12z + z2 = 0 + 146

Combine like terms: 0 + 146 = 146
12z + z2 = 146

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 = 146 + 36

Reorder the terms:
36 + 12z + z2 = 146 + 36

Combine like terms: 146 + 36 = 182
36 + 12z + z2 = 182

Factor a perfect square on the left side:
(z + 6)(z + 6) = 182

Calculate the square root of the right side: 13.490737563

Break this problem into two subproblems by setting 
(z + 6) equal to 13.490737563 and -13.490737563.

Subproblem 1
z + 6 = 13.490737563

Simplifying
z + 6 = 13.490737563

Reorder the terms:
6 + z = 13.490737563

Solving
6 + z = 13.490737563

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 = 13.490737563 + -6

Combine like terms: 6 + -6 = 0
0 + z = 13.490737563 + -6
z = 13.490737563 + -6

Combine like terms: 13.490737563 + -6 = 7.490737563
z = 7.490737563

Simplifying
z = 7.490737563

Subproblem 2
z + 6 = -13.490737563

Simplifying
z + 6 = -13.490737563

Reorder the terms:
6 + z = -13.490737563

Solving
6 + z = -13.490737563

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 = -13.490737563 + -6

Combine like terms: 6 + -6 = 0
0 + z = -13.490737563 + -6
z = -13.490737563 + -6

Combine like terms: -13.490737563 + -6 = -19.490737563
z = -19.490737563

Simplifying
z = -19.490737563

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {7.490737563, -19.490737563}