-2x(8-3x)=6x+2

Solution for -2x(8-3x)=6x+2 equation:

Simplifying
-2x(8 + -3x) = 6x + 2
(8 * -2x + -3x * -2x) = 6x + 2
(-16x + 6x2) = 6x + 2

Reorder the terms:
-16x + 6x2 = 2 + 6x

Solving
-16x + 6x2 = 2 + 6x

Solving for variable 'x'.

Reorder the terms:
-2 + -16x + -6x + 6x2 = 2 + 6x + -2 + -6x

Combine like terms: -16x + -6x = -22x
-2 + -22x + 6x2 = 2 + 6x + -2 + -6x

Reorder the terms:
-2 + -22x + 6x2 = 2 + -2 + 6x + -6x

Combine like terms: 2 + -2 = 0
-2 + -22x + 6x2 = 0 + 6x + -6x
-2 + -22x + 6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + -22x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -11x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -11x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + -11x + 3x2 = 0

Solving
-1 + -11x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -3.666666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -3.666666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -3.666666667x + x2 = 0 + 0.3333333333
-3.666666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-3.666666667x + x2 = 0.3333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 0.3333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 0.3333333333 + 3.361111114

Combine like terms: 0.3333333333 + 3.361111114 = 3.6944444473
3.361111114 + -3.666666667x + x2 = 3.6944444473

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 3.6944444473

Calculate the square root of the right side: 1.922093767

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.922093767 and -1.922093767.

Subproblem 1
x + -1.833333334 = 1.922093767

Simplifying
x + -1.833333334 = 1.922093767

Reorder the terms:
-1.833333334 + x = 1.922093767

Solving
-1.833333334 + x = 1.922093767

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 1.922093767 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 1.922093767 + 1.833333334
x = 1.922093767 + 1.833333334

Combine like terms: 1.922093767 + 1.833333334 = 3.755427101
x = 3.755427101

Simplifying
x = 3.755427101

Subproblem 2
x + -1.833333334 = -1.922093767

Simplifying
x + -1.833333334 = -1.922093767

Reorder the terms:
-1.833333334 + x = -1.922093767

Solving
-1.833333334 + x = -1.922093767

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -1.922093767 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -1.922093767 + 1.833333334
x = -1.922093767 + 1.833333334

Combine like terms: -1.922093767 + 1.833333334 = -0.088760433
x = -0.088760433

Simplifying
x = -0.088760433

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.755427101, -0.088760433}
Solution
x = {3.755427101, -0.088760433}