z^2+9z-90=0

Solution for z^2+9z-90=0 equation:

Simplifying
z2 + 9z + -90 = 0

Reorder the terms:
-90 + 9z + z2 = 0

Solving
-90 + 9z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-15 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-15 + -1z)' equal to zero and attempt to solve:

Simplifying
-15 + -1z = 0

Solving
-15 + -1z = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1z = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1z = 0 + 15
-1z = 0 + 15

Combine like terms: 0 + 15 = 15
-1z = 15

Divide each side by '-1'.
z = -15

Simplifying
z = -15
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-15, 6}