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

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

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

Reorder the terms:
3x(-8 + 2x) + 2x = 8x + -4
(-8 * 3x + 2x * 3x) + 2x = 8x + -4
(-24x + 6x2) + 2x = 8x + -4

Reorder the terms:
-24x + 2x + 6x2 = 8x + -4

Combine like terms: -24x + 2x = -22x
-22x + 6x2 = 8x + -4

Reorder the terms:
-22x + 6x2 = -4 + 8x

Solving
-22x + 6x2 = -4 + 8x

Solving for variable 'x'.

Reorder the terms:
4 + -22x + -8x + 6x2 = -4 + 8x + 4 + -8x

Combine like terms: -22x + -8x = -30x
4 + -30x + 6x2 = -4 + 8x + 4 + -8x

Reorder the terms:
4 + -30x + 6x2 = -4 + 4 + 8x + -8x

Combine like terms: -4 + 4 = 0
4 + -30x + 6x2 = 0 + 8x + -8x
4 + -30x + 6x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
4 + -30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -15x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -15x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + -15x + 3x2 = 0

Solving
2 + -15x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -5x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -5x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -5x + x2 = 0 + -0.6666666667
-5x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-5x + x2 = -0.6666666667

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -0.6666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -0.6666666667 + 6.25

Combine like terms: -0.6666666667 + 6.25 = 5.5833333333
6.25 + -5x + x2 = 5.5833333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.5833333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.362907813 and -2.362907813.

Subproblem 1
x + -2.5 = 2.362907813

Simplifying
x + -2.5 = 2.362907813

Reorder the terms:
-2.5 + x = 2.362907813

Solving
-2.5 + x = 2.362907813

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.362907813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.362907813 + 2.5
x = 2.362907813 + 2.5

Combine like terms: 2.362907813 + 2.5 = 4.862907813
x = 4.862907813

Simplifying
x = 4.862907813

Subproblem 2
x + -2.5 = -2.362907813

Simplifying
x + -2.5 = -2.362907813

Reorder the terms:
-2.5 + x = -2.362907813

Solving
-2.5 + x = -2.362907813

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.362907813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.362907813 + 2.5
x = -2.362907813 + 2.5

Combine like terms: -2.362907813 + 2.5 = 0.137092187
x = 0.137092187

Simplifying
x = 0.137092187

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.862907813, 0.137092187}
Solution
x = {4.862907813, 0.137092187}