(x+3)(x+1)=24

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

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

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

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

Multiply (3 + x) * (1 + x)
(3(1 + x) + x(1 + x)) = 24
((1 * 3 + x * 3) + x(1 + x)) = 24
((3 + 3x) + x(1 + x)) = 24
(3 + 3x + (1 * x + x * x)) = 24
(3 + 3x + (1x + x2)) = 24

Combine like terms: 3x + 1x = 4x
(3 + 4x + x2) = 24

Solving
3 + 4x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
3 + -24 + 4x + x2 = 24 + -24

Combine like terms: 3 + -24 = -21
-21 + 4x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {-7, 3}