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

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

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

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

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

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

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

Solving
48 = 3 + 4x + x2

Solving for variable 'x'.

Combine like terms: 48 + -3 = 45
45 + -4x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2

Reorder the terms:
45 + -4x + -1x2 = 3 + -3 + 4x + -4x + x2 + -1x2

Combine like terms: 3 + -3 = 0
45 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
45 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
45 + -4x + -1x2 = 0 + x2 + -1x2
45 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + -4x + -1x2 = 0

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

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

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

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