a^2+3a+8a+24=

Solution for a^2+3a+8a+24= equation:

Simplifying
a2 + 3a + 8a + 24 = 0

Reorder the terms:
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}