(a+9)(a+3)=72

Solution for (a+9)(a+3)=72 equation:

Simplifying
(a + 9)(a + 3) = 72

Reorder the terms:
(9 + a)(a + 3) = 72

Reorder the terms:
(9 + a)(3 + a) = 72

Multiply (9 + a) * (3 + a)
(9(3 + a) + a(3 + a)) = 72
((3 * 9 + a * 9) + a(3 + a)) = 72
((27 + 9a) + a(3 + a)) = 72
(27 + 9a + (3 * a + a * a)) = 72
(27 + 9a + (3a + a2)) = 72

Combine like terms: 9a + 3a = 12a
(27 + 12a + a2) = 72

Solving
27 + 12a + a2 = 72

Solving for variable 'a'.

Reorder the terms:
27 + -72 + 12a + a2 = 72 + -72

Combine like terms: 27 + -72 = -45
-45 + 12a + a2 = 72 + -72

Combine like terms: 72 + -72 = 0
-45 + 12a + a2 = 0

Factor a trinomial.
(-15 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-15 + -1a)' equal to zero and attempt to solve:

Simplifying
-15 + -1a = 0

Solving
-15 + -1a = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1a = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1a = 0 + 15
-1a = 0 + 15

Combine like terms: 0 + 15 = 15
-1a = 15

Divide each side by '-1'.
a = -15

Simplifying
a = -15
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-15, 3}