(a+4)(a+8)=77

Solution for (a+4)(a+8)=77 equation:

Simplifying
(a + 4)(a + 8) = 77

Reorder the terms:
(4 + a)(a + 8) = 77

Reorder the terms:
(4 + a)(8 + a) = 77

Multiply (4 + a) * (8 + a)
(4(8 + a) + a(8 + a)) = 77
((8 * 4 + a * 4) + a(8 + a)) = 77
((32 + 4a) + a(8 + a)) = 77
(32 + 4a + (8 * a + a * a)) = 77
(32 + 4a + (8a + a2)) = 77

Combine like terms: 4a + 8a = 12a
(32 + 12a + a2) = 77

Solving
32 + 12a + a2 = 77

Solving for variable 'a'.

Reorder the terms:
32 + -77 + 12a + a2 = 77 + -77

Combine like terms: 32 + -77 = -45
-45 + 12a + a2 = 77 + -77

Combine like terms: 77 + -77 = 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}