(x+3)(x+1)=48

Solution for (x+3)(x+1)=48 equation:

Simplifying
(x + 3)(x + 1) = 48

Reorder the terms:
(3 + x)(x + 1) = 48

Reorder the terms:
(3 + x)(1 + x) = 48

Multiply (3 + x) * (1 + x)
(3(1 + x) + x(1 + x)) = 48
((1 * 3 + x * 3) + x(1 + x)) = 48
((3 + 3x) + x(1 + x)) = 48
(3 + 3x + (1 * x + x * x)) = 48
(3 + 3x + (1x + x2)) = 48

Combine like terms: 3x + 1x = 4x
(3 + 4x + x2) = 48

Solving
3 + 4x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
3 + -48 + 4x + x2 = 48 + -48

Combine like terms: 3 + -48 = -45
-45 + 4x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-45 + 4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Solution
x = {-9, 5}