(a+3)(2a+1)=0

Solution for (a+3)(2a+1)=0 equation:

Simplifying
(a + 3)(2a + 1) = 0

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

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

Multiply (3 + a) * (1 + 2a)
(3(1 + 2a) + a(1 + 2a)) = 0
((1 * 3 + 2a * 3) + a(1 + 2a)) = 0
((3 + 6a) + a(1 + 2a)) = 0
(3 + 6a + (1 * a + 2a * a)) = 0
(3 + 6a + (1a + 2a2)) = 0

Combine like terms: 6a + 1a = 7a
(3 + 7a + 2a2) = 0

Solving
3 + 7a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + a)(1 + 2a) = 0

Subproblem 1
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
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 = {-3, -0.5}