(a+4)(2a+1)=0

Solution for (a+4)(2a+1)=0 equation:

Simplifying
(a + 4)(2a + 1) = 0

Reorder the terms:
(4 + a)(2a + 1) = 0

Reorder the terms:
(4 + a)(1 + 2a) = 0

Multiply (4 + a) * (1 + 2a)
(4(1 + 2a) + a(1 + 2a)) = 0
((1 * 4 + 2a * 4) + a(1 + 2a)) = 0
((4 + 8a) + a(1 + 2a)) = 0
(4 + 8a + (1 * a + 2a * a)) = 0
(4 + 8a + (1a + 2a2)) = 0

Combine like terms: 8a + 1a = 9a
(4 + 9a + 2a2) = 0

Solving
4 + 9a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + a)(1 + 2a) = 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 '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-4, -0.5}