(x+8)(2x+14)=176+(x+15)

Solution for (x+8)(2x+14)=176+(x+15) equation:

Simplifying
(x + 8)(2x + 14) = 176 + (x + 15)

Reorder the terms:
(8 + x)(2x + 14) = 176 + (x + 15)

Reorder the terms:
(8 + x)(14 + 2x) = 176 + (x + 15)

Multiply (8 + x) * (14 + 2x)
(8(14 + 2x) + x(14 + 2x)) = 176 + (x + 15)
((14 * 8 + 2x * 8) + x(14 + 2x)) = 176 + (x + 15)
((112 + 16x) + x(14 + 2x)) = 176 + (x + 15)
(112 + 16x + (14 * x + 2x * x)) = 176 + (x + 15)
(112 + 16x + (14x + 2x2)) = 176 + (x + 15)

Combine like terms: 16x + 14x = 30x
(112 + 30x + 2x2) = 176 + (x + 15)

Reorder the terms:
112 + 30x + 2x2 = 176 + (15 + x)

Remove parenthesis around (15 + x)
112 + 30x + 2x2 = 176 + 15 + x

Combine like terms: 176 + 15 = 191
112 + 30x + 2x2 = 191 + x

Solving
112 + 30x + 2x2 = 191 + x

Solving for variable 'x'.

Reorder the terms:
112 + -191 + 30x + -1x + 2x2 = 191 + x + -191 + -1x

Combine like terms: 112 + -191 = -79
-79 + 30x + -1x + 2x2 = 191 + x + -191 + -1x

Combine like terms: 30x + -1x = 29x
-79 + 29x + 2x2 = 191 + x + -191 + -1x

Reorder the terms:
-79 + 29x + 2x2 = 191 + -191 + x + -1x

Combine like terms: 191 + -191 = 0
-79 + 29x + 2x2 = 0 + x + -1x
-79 + 29x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-79 + 29x + 2x2 = 0

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

Divide each side by '2'.
-39.5 + 14.5x + x2 = 0

Move the constant term to the right:

Add '39.5' to each side of the equation.
-39.5 + 14.5x + 39.5 + x2 = 0 + 39.5

Reorder the terms:
-39.5 + 39.5 + 14.5x + x2 = 0 + 39.5

Combine like terms: -39.5 + 39.5 = 0.0
0.0 + 14.5x + x2 = 0 + 39.5
14.5x + x2 = 0 + 39.5

Combine like terms: 0 + 39.5 = 39.5
14.5x + x2 = 39.5

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = 39.5 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = 39.5 + 52.5625

Combine like terms: 39.5 + 52.5625 = 92.0625
52.5625 + 14.5x + x2 = 92.0625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 92.0625

Calculate the square root of the right side: 9.594920531

Break this problem into two subproblems by setting 
(x + 7.25) equal to 9.594920531 and -9.594920531.

Subproblem 1
x + 7.25 = 9.594920531

Simplifying
x + 7.25 = 9.594920531

Reorder the terms:
7.25 + x = 9.594920531

Solving
7.25 + x = 9.594920531

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = 9.594920531 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = 9.594920531 + -7.25
x = 9.594920531 + -7.25

Combine like terms: 9.594920531 + -7.25 = 2.344920531
x = 2.344920531

Simplifying
x = 2.344920531

Subproblem 2
x + 7.25 = -9.594920531

Simplifying
x + 7.25 = -9.594920531

Reorder the terms:
7.25 + x = -9.594920531

Solving
7.25 + x = -9.594920531

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = -9.594920531 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = -9.594920531 + -7.25
x = -9.594920531 + -7.25

Combine like terms: -9.594920531 + -7.25 = -16.844920531
x = -16.844920531

Simplifying
x = -16.844920531

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.344920531, -16.844920531}