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

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

Simplifying
2(x + -8) + -3x(-8x + 4) = 0

Reorder the terms:
2(-8 + x) + -3x(-8x + 4) = 0
(-8 * 2 + x * 2) + -3x(-8x + 4) = 0
(-16 + 2x) + -3x(-8x + 4) = 0

Reorder the terms:
-16 + 2x + -3x(4 + -8x) = 0
-16 + 2x + (4 * -3x + -8x * -3x) = 0
-16 + 2x + (-12x + 24x2) = 0

Combine like terms: 2x + -12x = -10x
-16 + -10x + 24x2 = 0

Solving
-16 + -10x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -5x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -5x + 12x2)' equal to zero and attempt to solve:

Simplifying
-8 + -5x + 12x2 = 0

Solving
-8 + -5x + 12x2 = 0

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

Divide each side by '12'.
-0.6666666667 + -0.4166666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.4166666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.4166666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.4166666667x + x2 = 0 + 0.6666666667
-0.4166666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.4166666667x + x2 = 0.6666666667

The x term is -0.4166666667x.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667x + 0.04340277781 + x2 = 0.6666666667 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667x + x2 = 0.6666666667 + 0.04340277781

Combine like terms: 0.6666666667 + 0.04340277781 = 0.71006944451
0.04340277781 + -0.4166666667x + x2 = 0.71006944451

Factor a perfect square on the left side:
(x + -0.2083333334)(x + -0.2083333334) = 0.71006944451

Calculate the square root of the right side: 0.842656184

Break this problem into two subproblems by setting 
(x + -0.2083333334) equal to 0.842656184 and -0.842656184.

Subproblem 1
x + -0.2083333334 = 0.842656184

Simplifying
x + -0.2083333334 = 0.842656184

Reorder the terms:
-0.2083333334 + x = 0.842656184

Solving
-0.2083333334 + x = 0.842656184

Solving for variable 'x'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x = 0.842656184 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x = 0.842656184 + 0.2083333334
x = 0.842656184 + 0.2083333334

Combine like terms: 0.842656184 + 0.2083333334 = 1.0509895174
x = 1.0509895174

Simplifying
x = 1.0509895174

Subproblem 2
x + -0.2083333334 = -0.842656184

Simplifying
x + -0.2083333334 = -0.842656184

Reorder the terms:
-0.2083333334 + x = -0.842656184

Solving
-0.2083333334 + x = -0.842656184

Solving for variable 'x'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x = -0.842656184 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x = -0.842656184 + 0.2083333334
x = -0.842656184 + 0.2083333334

Combine like terms: -0.842656184 + 0.2083333334 = -0.6343228506
x = -0.6343228506

Simplifying
x = -0.6343228506

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0509895174, -0.6343228506}
Solution
x = {1.0509895174, -0.6343228506}