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

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

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

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

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

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

Combine like terms: 5z + 3z = 8z
(15 + 8z + z2) = 0

Solving
15 + 8z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + z)(3 + z) = 0

Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 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 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-5, -3}