(z+9)(z-5)=0

Solution for (z+9)(z-5)=0 equation:

Simplifying
(z + 9)(z + -5) = 0

Reorder the terms:
(9 + z)(z + -5) = 0

Reorder the terms:
(9 + z)(-5 + z) = 0

Multiply (9 + z) * (-5 + z)
(9(-5 + z) + z(-5 + z)) = 0
((-5 * 9 + z * 9) + z(-5 + z)) = 0
((-45 + 9z) + z(-5 + z)) = 0
(-45 + 9z + (-5 * z + z * z)) = 0
(-45 + 9z + (-5z + z2)) = 0

Combine like terms: 9z + -5z = 4z
(-45 + 4z + z2) = 0

Solving
-45 + 4z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -1z)(5 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve:

Simplifying
-9 + -1z = 0

Solving
-9 + -1z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1z = 0 + 9
-1z = 0 + 9

Combine like terms: 0 + 9 = 9
-1z = 9

Divide each side by '-1'.
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {-9, 5}