(2x+16)(2x)=42

Solution for (2x+16)(2x)=42 equation:

Simplifying
(2x + 16)(2x) = 42

Reorder the terms:
(16 + 2x)(2x) = 42

Remove parenthesis around (2x)
(16 + 2x) * 2x = 42

Reorder the terms for easier multiplication:
2x(16 + 2x) = 42
(16 * 2x + 2x * 2x) = 42
(32x + 4x2) = 42

Solving
32x + 4x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 32x + 4x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 16x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 16x + 2x2)' equal to zero and attempt to solve:

Simplifying
-21 + 16x + 2x2 = 0

Solving
-21 + 16x + 2x2 = 0

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

Divide each side by '2'.
-10.5 + 8x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + 8x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + 8x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + 8x + x2 = 0 + 10.5
8x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
8x + x2 = 10.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 10.5 + 16

Reorder the terms:
16 + 8x + x2 = 10.5 + 16

Combine like terms: 10.5 + 16 = 26.5
16 + 8x + x2 = 26.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 26.5

Calculate the square root of the right side: 5.14781507

Break this problem into two subproblems by setting 
(x + 4) equal to 5.14781507 and -5.14781507.

Subproblem 1
x + 4 = 5.14781507

Simplifying
x + 4 = 5.14781507

Reorder the terms:
4 + x = 5.14781507

Solving
4 + x = 5.14781507

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 5.14781507 + -4

Combine like terms: 4 + -4 = 0
0 + x = 5.14781507 + -4
x = 5.14781507 + -4

Combine like terms: 5.14781507 + -4 = 1.14781507
x = 1.14781507

Simplifying
x = 1.14781507

Subproblem 2
x + 4 = -5.14781507

Simplifying
x + 4 = -5.14781507

Reorder the terms:
4 + x = -5.14781507

Solving
4 + x = -5.14781507

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -5.14781507 + -4

Combine like terms: 4 + -4 = 0
0 + x = -5.14781507 + -4
x = -5.14781507 + -4

Combine like terms: -5.14781507 + -4 = -9.14781507
x = -9.14781507

Simplifying
x = -9.14781507

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.14781507, -9.14781507}
Solution
x = {1.14781507, -9.14781507}