8(x+1)=2x(x+16)

Solution for 8(x+1)=2x(x+16) equation:

Simplifying
8(x + 1) = 2x(x + 16)

Reorder the terms:
8(1 + x) = 2x(x + 16)
(1 * 8 + x * 8) = 2x(x + 16)
(8 + 8x) = 2x(x + 16)

Reorder the terms:
8 + 8x = 2x(16 + x)
8 + 8x = (16 * 2x + x * 2x)
8 + 8x = (32x + 2x2)

Solving
8 + 8x = 32x + 2x2

Solving for variable 'x'.

Combine like terms: 8x + -32x = -24x
8 + -24x + -2x2 = 32x + 2x2 + -32x + -2x2

Reorder the terms:
8 + -24x + -2x2 = 32x + -32x + 2x2 + -2x2

Combine like terms: 32x + -32x = 0
8 + -24x + -2x2 = 0 + 2x2 + -2x2
8 + -24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -12x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -12x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + -12x + -1x2 = 0

Solving
4 + -12x + -1x2 = 0

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

Divide each side by '-1'.
-4 + 12x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 12x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 12x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 12x + x2 = 0 + 4
12x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
12x + x2 = 4

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 = 4 + 36

Reorder the terms:
36 + 12x + x2 = 4 + 36

Combine like terms: 4 + 36 = 40
36 + 12x + x2 = 40

Factor a perfect square on the left side:
(x + 6)(x + 6) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 6) equal to 6.32455532 and -6.32455532.

Subproblem 1
x + 6 = 6.32455532

Simplifying
x + 6 = 6.32455532

Reorder the terms:
6 + x = 6.32455532

Solving
6 + x = 6.32455532

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 = 6.32455532 + -6

Combine like terms: 6 + -6 = 0
0 + x = 6.32455532 + -6
x = 6.32455532 + -6

Combine like terms: 6.32455532 + -6 = 0.32455532
x = 0.32455532

Simplifying
x = 0.32455532

Subproblem 2
x + 6 = -6.32455532

Simplifying
x + 6 = -6.32455532

Reorder the terms:
6 + x = -6.32455532

Solving
6 + x = -6.32455532

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 = -6.32455532 + -6

Combine like terms: 6 + -6 = 0
0 + x = -6.32455532 + -6
x = -6.32455532 + -6

Combine like terms: -6.32455532 + -6 = -12.32455532
x = -12.32455532

Simplifying
x = -12.32455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.32455532, -12.32455532}
Solution
x = {0.32455532, -12.32455532}