2(x-4)(7x-8)=8

Solution for 2(x-4)(7x-8)=8 equation:

Simplifying
2(x + -4)(7x + -8) = 8

Reorder the terms:
2(-4 + x)(7x + -8) = 8

Reorder the terms:
2(-4 + x)(-8 + 7x) = 8

Multiply (-4 + x) * (-8 + 7x)
2(-4(-8 + 7x) + x(-8 + 7x)) = 8
2((-8 * -4 + 7x * -4) + x(-8 + 7x)) = 8
2((32 + -28x) + x(-8 + 7x)) = 8
2(32 + -28x + (-8 * x + 7x * x)) = 8
2(32 + -28x + (-8x + 7x2)) = 8

Combine like terms: -28x + -8x = -36x
2(32 + -36x + 7x2) = 8
(32 * 2 + -36x * 2 + 7x2 * 2) = 8
(64 + -72x + 14x2) = 8

Solving
64 + -72x + 14x2 = 8

Solving for variable 'x'.

Reorder the terms:
64 + -8 + -72x + 14x2 = 8 + -8

Combine like terms: 64 + -8 = 56
56 + -72x + 14x2 = 8 + -8

Combine like terms: 8 + -8 = 0
56 + -72x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -36x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(28 + -36x + 7x2)' equal to zero and attempt to solve:

Simplifying
28 + -36x + 7x2 = 0

Solving
28 + -36x + 7x2 = 0

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

Divide each side by '7'.
4 + -5.142857143x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.142857143x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -5.142857143x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.142857143x + x2 = 0 + -4
-5.142857143x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.142857143x + x2 = -4

The x term is -5.142857143x.  Take half its coefficient (-2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
-5.142857143x + 6.612244901 + x2 = -4 + 6.612244901

Reorder the terms:
6.612244901 + -5.142857143x + x2 = -4 + 6.612244901

Combine like terms: -4 + 6.612244901 = 2.612244901
6.612244901 + -5.142857143x + x2 = 2.612244901

Factor a perfect square on the left side:
(x + -2.571428572)(x + -2.571428572) = 2.612244901

Calculate the square root of the right side: 1.616244072

Break this problem into two subproblems by setting 
(x + -2.571428572) equal to 1.616244072 and -1.616244072.

Subproblem 1
x + -2.571428572 = 1.616244072

Simplifying
x + -2.571428572 = 1.616244072

Reorder the terms:
-2.571428572 + x = 1.616244072

Solving
-2.571428572 + x = 1.616244072

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = 1.616244072 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = 1.616244072 + 2.571428572
x = 1.616244072 + 2.571428572

Combine like terms: 1.616244072 + 2.571428572 = 4.187672644
x = 4.187672644

Simplifying
x = 4.187672644

Subproblem 2
x + -2.571428572 = -1.616244072

Simplifying
x + -2.571428572 = -1.616244072

Reorder the terms:
-2.571428572 + x = -1.616244072

Solving
-2.571428572 + x = -1.616244072

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = -1.616244072 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = -1.616244072 + 2.571428572
x = -1.616244072 + 2.571428572

Combine like terms: -1.616244072 + 2.571428572 = 0.9551845
x = 0.9551845

Simplifying
x = 0.9551845

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.187672644, 0.9551845}
Solution
x = {4.187672644, 0.9551845}