(2+a)(a+3)=

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

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

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

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

Combine like terms: 2a + 3a = 5a
(6 + 5a + a2) = 0

Solving
6 + 5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + a)(2 + a) = 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 '(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 = {-3, -2}