a(a+4)+2a+8=

Solution for a(a+4)+2a+8= equation:

Simplifying
a(a + 4) + 2a + 8 = 0

Reorder the terms:
a(4 + a) + 2a + 8 = 0
(4 * a + a * a) + 2a + 8 = 0
(4a + a2) + 2a + 8 = 0

Reorder the terms:
8 + 4a + 2a + a2 = 0

Combine like terms: 4a + 2a = 6a
8 + 6a + a2 = 0

Solving
8 + 6a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + a)(2 + a) = 0

Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {-4, -2}