(z+3)(z-5)=0

Solution for (z+3)(z-5)=0 equation:

Simplifying
(z + 3)(z + -5) = 0

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

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

Multiply (3 + z) * (-5 + z)
(3(-5 + z) + z(-5 + z)) = 0
((-5 * 3 + z * 3) + z(-5 + z)) = 0
((-15 + 3z) + z(-5 + z)) = 0
(-15 + 3z + (-5 * z + z * z)) = 0
(-15 + 3z + (-5z + z2)) = 0

Combine like terms: 3z + -5z = -2z
(-15 + -2z + z2) = 0

Solving
-15 + -2z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(5 + -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 '(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 = {-3, 5}