36z+63=-3z^2

Solution for 36z+63=-3z^2 equation:

Simplifying
36z + 63 = -3z2

Reorder the terms:
63 + 36z = -3z2

Solving
63 + 36z = -3z2

Solving for variable 'z'.

Combine like terms: -3z2 + 3z2 = 0
63 + 36z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + 12z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(21 + 12z + z2)' equal to zero and attempt to solve:

Simplifying
21 + 12z + z2 = 0

Solving
21 + 12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 12z + -21 + z2 = 0 + -21

Reorder the terms:
21 + -21 + 12z + z2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 12z + z2 = 0 + -21
12z + z2 = 0 + -21

Combine like terms: 0 + -21 = -21
12z + z2 = -21

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 = -21 + 36

Reorder the terms:
36 + 12z + z2 = -21 + 36

Combine like terms: -21 + 36 = 15
36 + 12z + z2 = 15

Factor a perfect square on the left side:
(z + 6)(z + 6) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(z + 6) equal to 3.872983346 and -3.872983346.

Subproblem 1
z + 6 = 3.872983346

Simplifying
z + 6 = 3.872983346

Reorder the terms:
6 + z = 3.872983346

Solving
6 + z = 3.872983346

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 = 3.872983346 + -6

Combine like terms: 6 + -6 = 0
0 + z = 3.872983346 + -6
z = 3.872983346 + -6

Combine like terms: 3.872983346 + -6 = -2.127016654
z = -2.127016654

Simplifying
z = -2.127016654

Subproblem 2
z + 6 = -3.872983346

Simplifying
z + 6 = -3.872983346

Reorder the terms:
6 + z = -3.872983346

Solving
6 + z = -3.872983346

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 = -3.872983346 + -6

Combine like terms: 6 + -6 = 0
0 + z = -3.872983346 + -6
z = -3.872983346 + -6

Combine like terms: -3.872983346 + -6 = -9.872983346
z = -9.872983346

Simplifying
z = -9.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-2.127016654, -9.872983346}
Solution
z = {-2.127016654, -9.872983346}