-z^2-9z+36=0

Solution for -z^2-9z+36=0 equation:

Simplifying
-1z2 + -9z + 36 = 0

Reorder the terms:
36 + -9z + -1z2 = 0

Solving
36 + -9z + -1z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(12 + z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(12 + z)' equal to zero and attempt to solve:

Simplifying
12 + z = 0

Solving
12 + z = 0

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

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

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

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

Simplifying
z = -12
Solution
z = {3, -12}