(x+5)(x+3)=48

Solution for (x+5)(x+3)=48 equation:

Simplifying
(x + 5)(x + 3) = 48

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

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

Multiply (5 + x) * (3 + x)
(5(3 + x) + x(3 + x)) = 48
((3 * 5 + x * 5) + x(3 + x)) = 48
((15 + 5x) + x(3 + x)) = 48
(15 + 5x + (3 * x + x * x)) = 48
(15 + 5x + (3x + x2)) = 48

Combine like terms: 5x + 3x = 8x
(15 + 8x + x2) = 48

Solving
15 + 8x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
15 + -48 + 8x + x2 = 48 + -48

Combine like terms: 15 + -48 = -33
-33 + 8x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-33 + 8x + x2 = 0

Factor a trinomial.
(-11 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
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 = {-11, 3}