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

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

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

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

Reorder the terms:
-8 + 16x + 12x + 2x2 = 0

Combine like terms: 16x + 12x = 28x
-8 + 28x + 2x2 = 0

Solving
-8 + 28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 14x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + 14x + x2 = 0

Solving
-4 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 14x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 14x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 14x + x2 = 0 + 4
14x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
14x + x2 = 4

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 4 + 49

Reorder the terms:
49 + 14x + x2 = 4 + 49

Combine like terms: 4 + 49 = 53
49 + 14x + x2 = 53

Factor a perfect square on the left side:
(x + 7)(x + 7) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(x + 7) equal to 7.280109889 and -7.280109889.

Subproblem 1
x + 7 = 7.280109889

Simplifying
x + 7 = 7.280109889

Reorder the terms:
7 + x = 7.280109889

Solving
7 + x = 7.280109889

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 7.280109889 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.280109889 + -7
x = 7.280109889 + -7

Combine like terms: 7.280109889 + -7 = 0.280109889
x = 0.280109889

Simplifying
x = 0.280109889

Subproblem 2
x + 7 = -7.280109889

Simplifying
x + 7 = -7.280109889

Reorder the terms:
7 + x = -7.280109889

Solving
7 + x = -7.280109889

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -7.280109889 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.280109889 + -7
x = -7.280109889 + -7

Combine like terms: -7.280109889 + -7 = -14.280109889
x = -14.280109889

Simplifying
x = -14.280109889

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.280109889, -14.280109889}
Solution
x = {0.280109889, -14.280109889}