(a+3)(a+4)=72

Solution for (a+3)(a+4)=72 equation:

Simplifying
(a + 3)(a + 4) = 72

Reorder the terms:
(3 + a)(a + 4) = 72

Reorder the terms:
(3 + a)(4 + a) = 72

Multiply (3 + a) * (4 + a)
(3(4 + a) + a(4 + a)) = 72
((4 * 3 + a * 3) + a(4 + a)) = 72
((12 + 3a) + a(4 + a)) = 72
(12 + 3a + (4 * a + a * a)) = 72
(12 + 3a + (4a + a2)) = 72

Combine like terms: 3a + 4a = 7a
(12 + 7a + a2) = 72

Solving
12 + 7a + a2 = 72

Solving for variable 'a'.

Reorder the terms:
12 + -72 + 7a + a2 = 72 + -72

Combine like terms: 12 + -72 = -60
-60 + 7a + a2 = 72 + -72

Combine like terms: 72 + -72 = 0
-60 + 7a + a2 = 0

Factor a trinomial.
(-12 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-12 + -1a)' equal to zero and attempt to solve:

Simplifying
-12 + -1a = 0

Solving
-12 + -1a = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1a = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1a = 0 + 12
-1a = 0 + 12

Combine like terms: 0 + 12 = 12
-1a = 12

Divide each side by '-1'.
a = -12

Simplifying
a = -12
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-12, 5}