(a+1)(a+5)=0

Solution for (a+1)(a+5)=0 equation:

Simplifying
(a + 1)(a + 5) = 0

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

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

Multiply (1 + a) * (5 + a)
(1(5 + a) + a(5 + a)) = 0
((5 * 1 + a * 1) + a(5 + a)) = 0
((5 + 1a) + a(5 + a)) = 0
(5 + 1a + (5 * a + a * a)) = 0
(5 + 1a + (5a + a2)) = 0

Combine like terms: 1a + 5a = 6a
(5 + 6a + a2) = 0

Solving
5 + 6a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + a)(1 + 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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Solution
a = {-5, -1}