(a+3)(a+8)=84

Solution for (a+3)(a+8)=84 equation:

Simplifying
(a + 3)(a + 8) = 84

Reorder the terms:
(3 + a)(a + 8) = 84

Reorder the terms:
(3 + a)(8 + a) = 84

Multiply (3 + a) * (8 + a)
(3(8 + a) + a(8 + a)) = 84
((8 * 3 + a * 3) + a(8 + a)) = 84
((24 + 3a) + a(8 + a)) = 84
(24 + 3a + (8 * a + a * a)) = 84
(24 + 3a + (8a + a2)) = 84

Combine like terms: 3a + 8a = 11a
(24 + 11a + a2) = 84

Solving
24 + 11a + a2 = 84

Solving for variable 'a'.

Reorder the terms:
24 + -84 + 11a + a2 = 84 + -84

Combine like terms: 24 + -84 = -60
-60 + 11a + a2 = 84 + -84

Combine like terms: 84 + -84 = 0
-60 + 11a + a2 = 0

Factor a trinomial.
(-15 + -1a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-15, 4}