6x(-2x+1)=-11(x+1)

Solution for 6x(-2x+1)=-11(x+1) equation:

Simplifying
6x(-2x + 1) = -11(x + 1)

Reorder the terms:
6x(1 + -2x) = -11(x + 1)
(1 * 6x + -2x * 6x) = -11(x + 1)
(6x + -12x2) = -11(x + 1)

Reorder the terms:
6x + -12x2 = -11(1 + x)
6x + -12x2 = (1 * -11 + x * -11)
6x + -12x2 = (-11 + -11x)

Solving
6x + -12x2 = -11 + -11x

Solving for variable 'x'.

Reorder the terms:
11 + 6x + 11x + -12x2 = -11 + -11x + 11 + 11x

Combine like terms: 6x + 11x = 17x
11 + 17x + -12x2 = -11 + -11x + 11 + 11x

Reorder the terms:
11 + 17x + -12x2 = -11 + 11 + -11x + 11x

Combine like terms: -11 + 11 = 0
11 + 17x + -12x2 = 0 + -11x + 11x
11 + 17x + -12x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
11 + 17x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.9166666667 + -1.416666667x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + -1.416666667x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + -1.416666667x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + -1.416666667x + x2 = 0 + 0.9166666667
-1.416666667x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
-1.416666667x + x2 = 0.9166666667

The x term is -1.416666667x.  Take half its coefficient (-0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
-1.416666667x + 0.5017361113 + x2 = 0.9166666667 + 0.5017361113

Reorder the terms:
0.5017361113 + -1.416666667x + x2 = 0.9166666667 + 0.5017361113

Combine like terms: 0.9166666667 + 0.5017361113 = 1.418402778
0.5017361113 + -1.416666667x + x2 = 1.418402778

Factor a perfect square on the left side:
(x + -0.7083333335)(x + -0.7083333335) = 1.418402778

Calculate the square root of the right side: 1.190967161

Break this problem into two subproblems by setting 
(x + -0.7083333335) equal to 1.190967161 and -1.190967161.

Subproblem 1
x + -0.7083333335 = 1.190967161

Simplifying
x + -0.7083333335 = 1.190967161

Reorder the terms:
-0.7083333335 + x = 1.190967161

Solving
-0.7083333335 + x = 1.190967161

Solving for variable 'x'.

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

Add '0.7083333335' to each side of the equation.
-0.7083333335 + 0.7083333335 + x = 1.190967161 + 0.7083333335

Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000
0.0000000000 + x = 1.190967161 + 0.7083333335
x = 1.190967161 + 0.7083333335

Combine like terms: 1.190967161 + 0.7083333335 = 1.8993004945
x = 1.8993004945

Simplifying
x = 1.8993004945

Subproblem 2
x + -0.7083333335 = -1.190967161

Simplifying
x + -0.7083333335 = -1.190967161

Reorder the terms:
-0.7083333335 + x = -1.190967161

Solving
-0.7083333335 + x = -1.190967161

Solving for variable 'x'.

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

Add '0.7083333335' to each side of the equation.
-0.7083333335 + 0.7083333335 + x = -1.190967161 + 0.7083333335

Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000
0.0000000000 + x = -1.190967161 + 0.7083333335
x = -1.190967161 + 0.7083333335

Combine like terms: -1.190967161 + 0.7083333335 = -0.4826338275
x = -0.4826338275

Simplifying
x = -0.4826338275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8993004945, -0.4826338275}