(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.
(-9 + -1z)(3 + -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 '(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 = {-9, 3}