(x+3)(2x+8)=42

Solution for (x+3)(2x+8)=42 equation:

Simplifying
(x + 3)(2x + 8) = 42

Reorder the terms:
(3 + x)(2x + 8) = 42

Reorder the terms:
(3 + x)(8 + 2x) = 42

Multiply (3 + x) * (8 + 2x)
(3(8 + 2x) + x(8 + 2x)) = 42
((8 * 3 + 2x * 3) + x(8 + 2x)) = 42
((24 + 6x) + x(8 + 2x)) = 42
(24 + 6x + (8 * x + 2x * x)) = 42
(24 + 6x + (8x + 2x2)) = 42

Combine like terms: 6x + 8x = 14x
(24 + 14x + 2x2) = 42

Solving
24 + 14x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
24 + -42 + 14x + 2x2 = 42 + -42

Combine like terms: 24 + -42 = -18
-18 + 14x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-18 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 7x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 7x + x2 = 0

Solving
-9 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 7x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 7x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 7x + x2 = 0 + 9
7x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
7x + x2 = 9

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 9 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 9 + 12.25

Combine like terms: 9 + 12.25 = 21.25
12.25 + 7x + x2 = 21.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
x + 3.5 = 4.609772229

Simplifying
x + 3.5 = 4.609772229

Reorder the terms:
3.5 + x = 4.609772229

Solving
3.5 + x = 4.609772229

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.609772229 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.609772229 + -3.5
x = 4.609772229 + -3.5

Combine like terms: 4.609772229 + -3.5 = 1.109772229
x = 1.109772229

Simplifying
x = 1.109772229

Subproblem 2
x + 3.5 = -4.609772229

Simplifying
x + 3.5 = -4.609772229

Reorder the terms:
3.5 + x = -4.609772229

Solving
3.5 + x = -4.609772229

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.609772229 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.609772229 + -3.5
x = -4.609772229 + -3.5

Combine like terms: -4.609772229 + -3.5 = -8.109772229
x = -8.109772229

Simplifying
x = -8.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.109772229, -8.109772229}
Solution
x = {1.109772229, -8.109772229}