(a+2)(a+3)=20

Solution for (a+2)(a+3)=20 equation:

Simplifying
(a + 2)(a + 3) = 20

Reorder the terms:
(2 + a)(a + 3) = 20

Reorder the terms:
(2 + a)(3 + a) = 20

Multiply (2 + a) * (3 + a)
(2(3 + a) + a(3 + a)) = 20
((3 * 2 + a * 2) + a(3 + a)) = 20
((6 + 2a) + a(3 + a)) = 20
(6 + 2a + (3 * a + a * a)) = 20
(6 + 2a + (3a + a2)) = 20

Combine like terms: 2a + 3a = 5a
(6 + 5a + a2) = 20

Solving
6 + 5a + a2 = 20

Solving for variable 'a'.

Reorder the terms:
6 + -20 + 5a + a2 = 20 + -20

Combine like terms: 6 + -20 = -14
-14 + 5a + a2 = 20 + -20

Combine like terms: 20 + -20 = 0
-14 + 5a + a2 = 0

Factor a trinomial.
(-7 + -1a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-7, 2}