8(14)=(x+8)(2x+8)

Solution for 8(14)=(x+8)(2x+8) equation:

Simplifying
8(14) = (x + 8)(2x + 8)

Multiply 8 * 14
112 = (x + 8)(2x + 8)

Reorder the terms:
112 = (8 + x)(2x + 8)

Reorder the terms:
112 = (8 + x)(8 + 2x)

Multiply (8 + x) * (8 + 2x)
112 = (8(8 + 2x) + x(8 + 2x))
112 = ((8 * 8 + 2x * 8) + x(8 + 2x))
112 = ((64 + 16x) + x(8 + 2x))
112 = (64 + 16x + (8 * x + 2x * x))
112 = (64 + 16x + (8x + 2x2))

Combine like terms: 16x + 8x = 24x
112 = (64 + 24x + 2x2)

Solving
112 = 64 + 24x + 2x2

Solving for variable 'x'.

Combine like terms: 112 + -64 = 48
48 + -24x + -2x2 = 64 + 24x + 2x2 + -64 + -24x + -2x2

Reorder the terms:
48 + -24x + -2x2 = 64 + -64 + 24x + -24x + 2x2 + -2x2

Combine like terms: 64 + -64 = 0
48 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2
48 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2

Combine like terms: 24x + -24x = 0
48 + -24x + -2x2 = 0 + 2x2 + -2x2
48 + -24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
48 + -24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -12x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(24 + -12x + -1x2)' equal to zero and attempt to solve:

Simplifying
24 + -12x + -1x2 = 0

Solving
24 + -12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-24 + 12x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 12x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 12x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 12x + x2 = 0 + 24
12x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
12x + x2 = 24

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 = 24 + 36

Reorder the terms:
36 + 12x + x2 = 24 + 36

Combine like terms: 24 + 36 = 60
36 + 12x + x2 = 60

Factor a perfect square on the left side:
(x + 6)(x + 6) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 6) equal to 7.745966692 and -7.745966692.

Subproblem 1
x + 6 = 7.745966692

Simplifying
x + 6 = 7.745966692

Reorder the terms:
6 + x = 7.745966692

Solving
6 + x = 7.745966692

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 = 7.745966692 + -6

Combine like terms: 6 + -6 = 0
0 + x = 7.745966692 + -6
x = 7.745966692 + -6

Combine like terms: 7.745966692 + -6 = 1.745966692
x = 1.745966692

Simplifying
x = 1.745966692

Subproblem 2
x + 6 = -7.745966692

Simplifying
x + 6 = -7.745966692

Reorder the terms:
6 + x = -7.745966692

Solving
6 + x = -7.745966692

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 = -7.745966692 + -6

Combine like terms: 6 + -6 = 0
0 + x = -7.745966692 + -6
x = -7.745966692 + -6

Combine like terms: -7.745966692 + -6 = -13.745966692
x = -13.745966692

Simplifying
x = -13.745966692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.745966692, -13.745966692}
Solution
x = {1.745966692, -13.745966692}