17x(-8)(2x-4)=32

Solution for 17x(-8)(2x-4)=32 equation:

Simplifying
17x(-8)(2x + -4) = 32

Reorder the terms:
17x * -8(-4 + 2x) = 32

Reorder the terms for easier multiplication:
17 * -8x(-4 + 2x) = 32

Multiply 17 * -8
-136x(-4 + 2x) = 32
(-4 * -136x + 2x * -136x) = 32
(544x + -272x2) = 32

Solving
544x + -272x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 544x + -272x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 544x + -272x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + 34x + -17x2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-2 + 34x + -17x2)' equal to zero and attempt to solve:

Simplifying
-2 + 34x + -17x2 = 0

Solving
-2 + 34x + -17x2 = 0

Begin completing the square.  Divide all terms by
-17 the coefficient of the squared term: 

Divide each side by '-17'.
0.1176470588 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.1176470588' to each side of the equation.
0.1176470588 + -2x + -0.1176470588 + x2 = 0 + -0.1176470588

Reorder the terms:
0.1176470588 + -0.1176470588 + -2x + x2 = 0 + -0.1176470588

Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.1176470588
-2x + x2 = 0 + -0.1176470588

Combine like terms: 0 + -0.1176470588 = -0.1176470588
-2x + x2 = -0.1176470588

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.1176470588 + 1

Reorder the terms:
1 + -2x + x2 = -0.1176470588 + 1

Combine like terms: -0.1176470588 + 1 = 0.8823529412
1 + -2x + x2 = 0.8823529412

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.8823529412

Calculate the square root of the right side: 0.939336437

Break this problem into two subproblems by setting 
(x + -1) equal to 0.939336437 and -0.939336437.

Subproblem 1
x + -1 = 0.939336437

Simplifying
x + -1 = 0.939336437

Reorder the terms:
-1 + x = 0.939336437

Solving
-1 + x = 0.939336437

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.939336437 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.939336437 + 1
x = 0.939336437 + 1

Combine like terms: 0.939336437 + 1 = 1.939336437
x = 1.939336437

Simplifying
x = 1.939336437

Subproblem 2
x + -1 = -0.939336437

Simplifying
x + -1 = -0.939336437

Reorder the terms:
-1 + x = -0.939336437

Solving
-1 + x = -0.939336437

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.939336437 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.939336437 + 1
x = -0.939336437 + 1

Combine like terms: -0.939336437 + 1 = 0.060663563
x = 0.060663563

Simplifying
x = 0.060663563

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.939336437, 0.060663563}
Solution
x = {1.939336437, 0.060663563}