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.
(-12 + -1Z)(3 + -1Z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
Z = {-12, 3}