(z-3)(z+5)=9

Solution for (z-3)(z+5)=9 equation:

Simplifying
(z + -3)(z + 5) = 9

Reorder the terms:
(-3 + z)(z + 5) = 9

Reorder the terms:
(-3 + z)(5 + z) = 9

Multiply (-3 + z) * (5 + z)
(-3(5 + z) + z(5 + z)) = 9
((5 * -3 + z * -3) + z(5 + z)) = 9
((-15 + -3z) + z(5 + z)) = 9
(-15 + -3z + (5 * z + z * z)) = 9
(-15 + -3z + (5z + z2)) = 9

Combine like terms: -3z + 5z = 2z
(-15 + 2z + z2) = 9

Solving
-15 + 2z + z2 = 9

Solving for variable 'z'.

Reorder the terms:
-15 + -9 + 2z + z2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + 2z + z2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + 2z + z2 = 0

Factor a trinomial.
(-6 + -1z)(4 + -1z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-6, 4}