3(2+6x)-8x(x-5)=4(3x+2)

Solution for 3(2+6x)-8x(x-5)=4(3x+2) equation:

Simplifying
3(2 + 6x) + -8x(x + -5) = 4(3x + 2)
(2 * 3 + 6x * 3) + -8x(x + -5) = 4(3x + 2)
(6 + 18x) + -8x(x + -5) = 4(3x + 2)

Reorder the terms:
6 + 18x + -8x(-5 + x) = 4(3x + 2)
6 + 18x + (-5 * -8x + x * -8x) = 4(3x + 2)
6 + 18x + (40x + -8x2) = 4(3x + 2)

Combine like terms: 18x + 40x = 58x
6 + 58x + -8x2 = 4(3x + 2)

Reorder the terms:
6 + 58x + -8x2 = 4(2 + 3x)
6 + 58x + -8x2 = (2 * 4 + 3x * 4)
6 + 58x + -8x2 = (8 + 12x)

Solving
6 + 58x + -8x2 = 8 + 12x

Solving for variable 'x'.

Reorder the terms:
6 + -8 + 58x + -12x + -8x2 = 8 + 12x + -8 + -12x

Combine like terms: 6 + -8 = -2
-2 + 58x + -12x + -8x2 = 8 + 12x + -8 + -12x

Combine like terms: 58x + -12x = 46x
-2 + 46x + -8x2 = 8 + 12x + -8 + -12x

Reorder the terms:
-2 + 46x + -8x2 = 8 + -8 + 12x + -12x

Combine like terms: 8 + -8 = 0
-2 + 46x + -8x2 = 0 + 12x + -12x
-2 + 46x + -8x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-2 + 46x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 23x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 23x + -4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 23x + -4x2 = 0

Solving
-1 + 23x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -5.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -5.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -5.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -5.75x + x2 = 0 + -0.25
-5.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-5.75x + x2 = -0.25

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = -0.25 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = -0.25 + 8.265625

Combine like terms: -0.25 + 8.265625 = 8.015625
8.265625 + -5.75x + x2 = 8.015625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 8.015625

Calculate the square root of the right side: 2.831187913

Break this problem into two subproblems by setting 
(x + -2.875) equal to 2.831187913 and -2.831187913.

Subproblem 1
x + -2.875 = 2.831187913

Simplifying
x + -2.875 = 2.831187913

Reorder the terms:
-2.875 + x = 2.831187913

Solving
-2.875 + x = 2.831187913

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = 2.831187913 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = 2.831187913 + 2.875
x = 2.831187913 + 2.875

Combine like terms: 2.831187913 + 2.875 = 5.706187913
x = 5.706187913

Simplifying
x = 5.706187913

Subproblem 2
x + -2.875 = -2.831187913

Simplifying
x + -2.875 = -2.831187913

Reorder the terms:
-2.875 + x = -2.831187913

Solving
-2.875 + x = -2.831187913

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = -2.831187913 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = -2.831187913 + 2.875
x = -2.831187913 + 2.875

Combine like terms: -2.831187913 + 2.875 = 0.043812087
x = 0.043812087

Simplifying
x = 0.043812087

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.706187913, 0.043812087}
Solution
x = {5.706187913, 0.043812087}