(a+3)(a+5)=0

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

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

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

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

Multiply (3 + a) * (5 + a)
(3(5 + a) + a(5 + a)) = 0
((5 * 3 + a * 3) + a(5 + a)) = 0
((15 + 3a) + a(5 + a)) = 0
(15 + 3a + (5 * a + a * a)) = 0
(15 + 3a + (5a + a2)) = 0

Combine like terms: 3a + 5a = 8a
(15 + 8a + a2) = 0

Solving
15 + 8a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
5 + a = 0

Solving
5 + a = 0

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

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

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

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

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

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

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

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

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