(z-9)(z+3)=0

Solution for (z-9)(z+3)=0 equation:

Simplifying
(z + -9)(z + 3) = 0

Reorder the terms:
(-9 + z)(z + 3) = 0

Reorder the terms:
(-9 + z)(3 + z) = 0

Multiply (-9 + z) * (3 + z)
(-9(3 + z) + z(3 + z)) = 0
((3 * -9 + z * -9) + z(3 + z)) = 0
((-27 + -9z) + z(3 + z)) = 0
(-27 + -9z + (3 * z + z * z)) = 0
(-27 + -9z + (3z + z2)) = 0

Combine like terms: -9z + 3z = -6z
(-27 + -6z + z2) = 0

Solving
-27 + -6z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(9 + -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 '(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
Solution
z = {-3, 9}