2x+16=4(x+4)2x

Solution for 2x+16=4(x+4)2x equation:

Simplifying
2x + 16 = 4(x + 4) * 2x

Reorder the terms:
16 + 2x = 4(x + 4) * 2x

Reorder the terms:
16 + 2x = 4(4 + x) * 2x

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

Multiply 4 * 2
16 + 2x = 8x(4 + x)
16 + 2x = (4 * 8x + x * 8x)
16 + 2x = (32x + 8x2)

Solving
16 + 2x = 32x + 8x2

Solving for variable 'x'.

Combine like terms: 2x + -32x = -30x
16 + -30x + -8x2 = 32x + 8x2 + -32x + -8x2

Reorder the terms:
16 + -30x + -8x2 = 32x + -32x + 8x2 + -8x2

Combine like terms: 32x + -32x = 0
16 + -30x + -8x2 = 0 + 8x2 + -8x2
16 + -30x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
16 + -30x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -15x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -15x + -4x2)' equal to zero and attempt to solve:

Simplifying
8 + -15x + -4x2 = 0

Solving
8 + -15x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2 + 3.75x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3.75x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3.75x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3.75x + x2 = 0 + 2
3.75x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3.75x + x2 = 2

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = 2 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = 2 + 3.515625

Combine like terms: 2 + 3.515625 = 5.515625
3.515625 + 3.75x + x2 = 5.515625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 5.515625

Calculate the square root of the right side: 2.348536779

Break this problem into two subproblems by setting 
(x + 1.875) equal to 2.348536779 and -2.348536779.

Subproblem 1
x + 1.875 = 2.348536779

Simplifying
x + 1.875 = 2.348536779

Reorder the terms:
1.875 + x = 2.348536779

Solving
1.875 + x = 2.348536779

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = 2.348536779 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = 2.348536779 + -1.875
x = 2.348536779 + -1.875

Combine like terms: 2.348536779 + -1.875 = 0.473536779
x = 0.473536779

Simplifying
x = 0.473536779

Subproblem 2
x + 1.875 = -2.348536779

Simplifying
x + 1.875 = -2.348536779

Reorder the terms:
1.875 + x = -2.348536779

Solving
1.875 + x = -2.348536779

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = -2.348536779 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = -2.348536779 + -1.875
x = -2.348536779 + -1.875

Combine like terms: -2.348536779 + -1.875 = -4.223536779
x = -4.223536779

Simplifying
x = -4.223536779

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.473536779, -4.223536779}
Solution
x = {0.473536779, -4.223536779}