(2x-4)(3x+8)=16

Solution for (2x-4)(3x+8)=16 equation:

Simplifying
(2x + -4)(3x + 8) = 16

Reorder the terms:
(-4 + 2x)(3x + 8) = 16

Reorder the terms:
(-4 + 2x)(8 + 3x) = 16

Multiply (-4 + 2x) * (8 + 3x)
(-4(8 + 3x) + 2x * (8 + 3x)) = 16
((8 * -4 + 3x * -4) + 2x * (8 + 3x)) = 16
((-32 + -12x) + 2x * (8 + 3x)) = 16
(-32 + -12x + (8 * 2x + 3x * 2x)) = 16
(-32 + -12x + (16x + 6x2)) = 16

Combine like terms: -12x + 16x = 4x
(-32 + 4x + 6x2) = 16

Solving
-32 + 4x + 6x2 = 16

Solving for variable 'x'.

Reorder the terms:
-32 + -16 + 4x + 6x2 = 16 + -16

Combine like terms: -32 + -16 = -48
-48 + 4x + 6x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-48 + 4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 2x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
-24 + 2x + 3x2 = 0

Solving
-24 + 2x + 3x2 = 0

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

Divide each side by '3'.
-8 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 0.6666666667x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 0.6666666667x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 0.6666666667x + x2 = 0 + 8
0.6666666667x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
0.6666666667x + x2 = 8

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 8 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 8 + 0.1111111112

Combine like terms: 8 + 0.1111111112 = 8.1111111112
0.1111111112 + 0.6666666667x + x2 = 8.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 8.1111111112

Calculate the square root of the right side: 2.848001248

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 2.848001248 and -2.848001248.

Subproblem 1
x + 0.3333333334 = 2.848001248

Simplifying
x + 0.3333333334 = 2.848001248

Reorder the terms:
0.3333333334 + x = 2.848001248

Solving
0.3333333334 + x = 2.848001248

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 2.848001248 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 2.848001248 + -0.3333333334
x = 2.848001248 + -0.3333333334

Combine like terms: 2.848001248 + -0.3333333334 = 2.5146679146
x = 2.5146679146

Simplifying
x = 2.5146679146

Subproblem 2
x + 0.3333333334 = -2.848001248

Simplifying
x + 0.3333333334 = -2.848001248

Reorder the terms:
0.3333333334 + x = -2.848001248

Solving
0.3333333334 + x = -2.848001248

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -2.848001248 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -2.848001248 + -0.3333333334
x = -2.848001248 + -0.3333333334

Combine like terms: -2.848001248 + -0.3333333334 = -3.1813345814
x = -3.1813345814

Simplifying
x = -3.1813345814

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5146679146, -3.1813345814}
Solution
x = {2.5146679146, -3.1813345814}