(a+3)(a+8)=0

Solution for (a+3)(a+8)=0 equation:

Simplifying
(a + 3)(a + 8) = 0

Reorder the terms:
(3 + a)(a + 8) = 0

Reorder the terms:
(3 + a)(8 + a) = 0

Multiply (3 + a) * (8 + a)
(3(8 + a) + a(8 + a)) = 0
((8 * 3 + a * 3) + a(8 + a)) = 0
((24 + 3a) + a(8 + a)) = 0
(24 + 3a + (8 * a + a * a)) = 0
(24 + 3a + (8a + a2)) = 0

Combine like terms: 3a + 8a = 11a
(24 + 11a + a2) = 0

Solving
24 + 11a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve:

Simplifying
8 + a = 0

Solving
8 + a = 0

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

Add '-8' to each side of the equation.
8 + -8 + a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + a = 0 + -8
a = 0 + -8

Combine like terms: 0 + -8 = -8
a = -8

Simplifying
a = -8
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 = {-8, -3}