(a+3)(2a+3)=5

Solution for (a+3)(2a+3)=5 equation:

Simplifying
(a + 3)(2a + 3) = 5

Reorder the terms:
(3 + a)(2a + 3) = 5

Reorder the terms:
(3 + a)(3 + 2a) = 5

Multiply (3 + a) * (3 + 2a)
(3(3 + 2a) + a(3 + 2a)) = 5
((3 * 3 + 2a * 3) + a(3 + 2a)) = 5
((9 + 6a) + a(3 + 2a)) = 5
(9 + 6a + (3 * a + 2a * a)) = 5
(9 + 6a + (3a + 2a2)) = 5

Combine like terms: 6a + 3a = 9a
(9 + 9a + 2a2) = 5

Solving
9 + 9a + 2a2 = 5

Solving for variable 'a'.

Reorder the terms:
9 + -5 + 9a + 2a2 = 5 + -5

Combine like terms: 9 + -5 = 4
4 + 9a + 2a2 = 5 + -5

Combine like terms: 5 + -5 = 0
4 + 9a + 2a2 = 0

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}