(x+8)(x+4)=42

Solution for (x+8)(x+4)=42 equation:

Simplifying
(x + 8)(x + 4) = 42

Reorder the terms:
(8 + x)(x + 4) = 42

Reorder the terms:
(8 + x)(4 + x) = 42

Multiply (8 + x) * (4 + x)
(8(4 + x) + x(4 + x)) = 42
((4 * 8 + x * 8) + x(4 + x)) = 42
((32 + 8x) + x(4 + x)) = 42
(32 + 8x + (4 * x + x * x)) = 42
(32 + 8x + (4x + x2)) = 42

Combine like terms: 8x + 4x = 12x
(32 + 12x + x2) = 42

Solving
32 + 12x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
32 + -42 + 12x + x2 = 42 + -42

Combine like terms: 32 + -42 = -10
-10 + 12x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-10 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 12x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 12x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 12x + x2 = 0 + 10
12x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
12x + x2 = 10

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 10 + 36

Reorder the terms:
36 + 12x + x2 = 10 + 36

Combine like terms: 10 + 36 = 46
36 + 12x + x2 = 46

Factor a perfect square on the left side:
(x + 6)(x + 6) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 6) equal to 6.782329983 and -6.782329983.

Subproblem 1
x + 6 = 6.782329983

Simplifying
x + 6 = 6.782329983

Reorder the terms:
6 + x = 6.782329983

Solving
6 + x = 6.782329983

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 6.782329983 + -6

Combine like terms: 6 + -6 = 0
0 + x = 6.782329983 + -6
x = 6.782329983 + -6

Combine like terms: 6.782329983 + -6 = 0.782329983
x = 0.782329983

Simplifying
x = 0.782329983

Subproblem 2
x + 6 = -6.782329983

Simplifying
x + 6 = -6.782329983

Reorder the terms:
6 + x = -6.782329983

Solving
6 + x = -6.782329983

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -6.782329983 + -6

Combine like terms: 6 + -6 = 0
0 + x = -6.782329983 + -6
x = -6.782329983 + -6

Combine like terms: -6.782329983 + -6 = -12.782329983
x = -12.782329983

Simplifying
x = -12.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.782329983, -12.782329983}