6+x(6x+1)=6(4x-1)

Solution for 6+x(6x+1)=6(4x-1) equation:

Simplifying
6 + x(6x + 1) = 6(4x + -1)

Reorder the terms:
6 + x(1 + 6x) = 6(4x + -1)
6 + (1 * x + 6x * x) = 6(4x + -1)
6 + (1x + 6x2) = 6(4x + -1)

Reorder the terms:
6 + 1x + 6x2 = 6(-1 + 4x)
6 + 1x + 6x2 = (-1 * 6 + 4x * 6)
6 + 1x + 6x2 = (-6 + 24x)

Solving
6 + 1x + 6x2 = -6 + 24x

Solving for variable 'x'.

Reorder the terms:
6 + 6 + 1x + -24x + 6x2 = -6 + 24x + 6 + -24x

Combine like terms: 6 + 6 = 12
12 + 1x + -24x + 6x2 = -6 + 24x + 6 + -24x

Combine like terms: 1x + -24x = -23x
12 + -23x + 6x2 = -6 + 24x + 6 + -24x

Reorder the terms:
12 + -23x + 6x2 = -6 + 6 + 24x + -24x

Combine like terms: -6 + 6 = 0
12 + -23x + 6x2 = 0 + 24x + -24x
12 + -23x + 6x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
12 + -23x + 6x2 = 0

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

Divide each side by '6'.
2 + -3.833333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.833333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.833333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.833333333x + x2 = 0 + -2
-3.833333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.833333333x + x2 = -2

The x term is -3.833333333x.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333x + 3.673611112 + x2 = -2 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333x + x2 = -2 + 3.673611112

Combine like terms: -2 + 3.673611112 = 1.673611112
3.673611112 + -3.833333333x + x2 = 1.673611112

Factor a perfect square on the left side:
(x + -1.916666667)(x + -1.916666667) = 1.673611112

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + -1.916666667) equal to 1.293681225 and -1.293681225.

Subproblem 1
x + -1.916666667 = 1.293681225

Simplifying
x + -1.916666667 = 1.293681225

Reorder the terms:
-1.916666667 + x = 1.293681225

Solving
-1.916666667 + x = 1.293681225

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = 1.293681225 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = 1.293681225 + 1.916666667
x = 1.293681225 + 1.916666667

Combine like terms: 1.293681225 + 1.916666667 = 3.210347892
x = 3.210347892

Simplifying
x = 3.210347892

Subproblem 2
x + -1.916666667 = -1.293681225

Simplifying
x + -1.916666667 = -1.293681225

Reorder the terms:
-1.916666667 + x = -1.293681225

Solving
-1.916666667 + x = -1.293681225

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = -1.293681225 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = -1.293681225 + 1.916666667
x = -1.293681225 + 1.916666667

Combine like terms: -1.293681225 + 1.916666667 = 0.622985442
x = 0.622985442

Simplifying
x = 0.622985442

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.210347892, 0.622985442}