(z-9)(z+3)=-32

Solution for (z-9)(z+3)=-32 equation:

Simplifying
(z + -9)(z + 3) = -32

Reorder the terms:
(-9 + z)(z + 3) = -32

Reorder the terms:
(-9 + z)(3 + z) = -32

Multiply (-9 + z) * (3 + z)
(-9(3 + z) + z(3 + z)) = -32
((3 * -9 + z * -9) + z(3 + z)) = -32
((-27 + -9z) + z(3 + z)) = -32
(-27 + -9z + (3 * z + z * z)) = -32
(-27 + -9z + (3z + z2)) = -32

Combine like terms: -9z + 3z = -6z
(-27 + -6z + z2) = -32

Solving
-27 + -6z + z2 = -32

Solving for variable 'z'.

Reorder the terms:
-27 + 32 + -6z + z2 = -32 + 32

Combine like terms: -27 + 32 = 5
5 + -6z + z2 = -32 + 32

Combine like terms: -32 + 32 = 0
5 + -6z + z2 = 0

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
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 = {1, 5}