6x-(2x+8)=3x(x+6)-14

Solution for 6x-(2x+8)=3x(x+6)-14 equation:

Simplifying
6x + -1(2x + 8) = 3x(x + 6) + -14

Reorder the terms:
6x + -1(8 + 2x) = 3x(x + 6) + -14
6x + (8 * -1 + 2x * -1) = 3x(x + 6) + -14
6x + (-8 + -2x) = 3x(x + 6) + -14

Reorder the terms:
-8 + 6x + -2x = 3x(x + 6) + -14

Combine like terms: 6x + -2x = 4x
-8 + 4x = 3x(x + 6) + -14

Reorder the terms:
-8 + 4x = 3x(6 + x) + -14
-8 + 4x = (6 * 3x + x * 3x) + -14
-8 + 4x = (18x + 3x2) + -14

Reorder the terms:
-8 + 4x = -14 + 18x + 3x2

Solving
-8 + 4x = -14 + 18x + 3x2

Solving for variable 'x'.

Reorder the terms:
-8 + 14 + 4x + -18x + -3x2 = -14 + 18x + 3x2 + 14 + -18x + -3x2

Combine like terms: -8 + 14 = 6
6 + 4x + -18x + -3x2 = -14 + 18x + 3x2 + 14 + -18x + -3x2

Combine like terms: 4x + -18x = -14x
6 + -14x + -3x2 = -14 + 18x + 3x2 + 14 + -18x + -3x2

Reorder the terms:
6 + -14x + -3x2 = -14 + 14 + 18x + -18x + 3x2 + -3x2

Combine like terms: -14 + 14 = 0
6 + -14x + -3x2 = 0 + 18x + -18x + 3x2 + -3x2
6 + -14x + -3x2 = 18x + -18x + 3x2 + -3x2

Combine like terms: 18x + -18x = 0
6 + -14x + -3x2 = 0 + 3x2 + -3x2
6 + -14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + -14x + -3x2 = 0

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

Divide each side by '-3'.
-2 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4.666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 4.666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4.666666667x + x2 = 0 + 2
4.666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
4.666666667x + x2 = 2

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 2 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 2 + 5.444444448

Combine like terms: 2 + 5.444444448 = 7.444444448
5.444444448 + 4.666666667x + x2 = 7.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 7.444444448

Calculate the square root of the right side: 2.728450925

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.728450925 and -2.728450925.

Subproblem 1
x + 2.333333334 = 2.728450925

Simplifying
x + 2.333333334 = 2.728450925

Reorder the terms:
2.333333334 + x = 2.728450925

Solving
2.333333334 + x = 2.728450925

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 2.728450925 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.728450925 + -2.333333334
x = 2.728450925 + -2.333333334

Combine like terms: 2.728450925 + -2.333333334 = 0.395117591
x = 0.395117591

Simplifying
x = 0.395117591

Subproblem 2
x + 2.333333334 = -2.728450925

Simplifying
x + 2.333333334 = -2.728450925

Reorder the terms:
2.333333334 + x = -2.728450925

Solving
2.333333334 + x = -2.728450925

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -2.728450925 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.728450925 + -2.333333334
x = -2.728450925 + -2.333333334

Combine like terms: -2.728450925 + -2.333333334 = -5.061784259
x = -5.061784259

Simplifying
x = -5.061784259

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.395117591, -5.061784259}