(a+1)(a+3)=24

Solution for (a+1)(a+3)=24 equation:

Simplifying
(a + 1)(a + 3) = 24

Reorder the terms:
(1 + a)(a + 3) = 24

Reorder the terms:
(1 + a)(3 + a) = 24

Multiply (1 + a) * (3 + a)
(1(3 + a) + a(3 + a)) = 24
((3 * 1 + a * 1) + a(3 + a)) = 24
((3 + 1a) + a(3 + a)) = 24
(3 + 1a + (3 * a + a * a)) = 24
(3 + 1a + (3a + a2)) = 24

Combine like terms: 1a + 3a = 4a
(3 + 4a + a2) = 24

Solving
3 + 4a + a2 = 24

Solving for variable 'a'.

Reorder the terms:
3 + -24 + 4a + a2 = 24 + -24

Combine like terms: 3 + -24 = -21
-21 + 4a + a2 = 24 + -24

Combine like terms: 24 + -24 = 0
-21 + 4a + a2 = 0

Factor a trinomial.
(-7 + -1a)(3 + -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 '(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 = {-7, 3}