z^2-9z-36=0

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

Simplifying
z2 + -9z + -36 = 0

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

Solving
-36 + -9z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(12 + -1z) = 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 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 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 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

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