=(2+a)(a+3)

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

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

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

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

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

Solving
0 = 6 + 5a + a2

Solving for variable 'a'.

Combine like terms: 0 + -6 = -6
-6 + -5a + -1a2 = 6 + 5a + a2 + -6 + -5a + -1a2

Reorder the terms:
-6 + -5a + -1a2 = 6 + -6 + 5a + -5a + a2 + -1a2

Combine like terms: 6 + -6 = 0
-6 + -5a + -1a2 = 0 + 5a + -5a + a2 + -1a2
-6 + -5a + -1a2 = 5a + -5a + a2 + -1a2

Combine like terms: 5a + -5a = 0
-6 + -5a + -1a2 = 0 + a2 + -1a2
-6 + -5a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-6 + -5a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5a + a2) = 0

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

Ignore the factor -1.
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}