-2x(3x+4)-x+6=-5x-2(x+1)+5

Solution for -2x(3x+4)-x+6=-5x-2(x+1)+5 equation:

Simplifying
-2x(3x + 4) + -1x + 6 = -5x + -2(x + 1) + 5

Reorder the terms:
-2x(4 + 3x) + -1x + 6 = -5x + -2(x + 1) + 5
(4 * -2x + 3x * -2x) + -1x + 6 = -5x + -2(x + 1) + 5
(-8x + -6x2) + -1x + 6 = -5x + -2(x + 1) + 5

Reorder the terms:
6 + -8x + -1x + -6x2 = -5x + -2(x + 1) + 5

Combine like terms: -8x + -1x = -9x
6 + -9x + -6x2 = -5x + -2(x + 1) + 5

Reorder the terms:
6 + -9x + -6x2 = -5x + -2(1 + x) + 5
6 + -9x + -6x2 = -5x + (1 * -2 + x * -2) + 5
6 + -9x + -6x2 = -5x + (-2 + -2x) + 5

Reorder the terms:
6 + -9x + -6x2 = -2 + 5 + -5x + -2x

Combine like terms: -2 + 5 = 3
6 + -9x + -6x2 = 3 + -5x + -2x

Combine like terms: -5x + -2x = -7x
6 + -9x + -6x2 = 3 + -7x

Solving
6 + -9x + -6x2 = 3 + -7x

Solving for variable 'x'.

Reorder the terms:
6 + -3 + -9x + 7x + -6x2 = 3 + -7x + -3 + 7x

Combine like terms: 6 + -3 = 3
3 + -9x + 7x + -6x2 = 3 + -7x + -3 + 7x

Combine like terms: -9x + 7x = -2x
3 + -2x + -6x2 = 3 + -7x + -3 + 7x

Reorder the terms:
3 + -2x + -6x2 = 3 + -3 + -7x + 7x

Combine like terms: 3 + -3 = 0
3 + -2x + -6x2 = 0 + -7x + 7x
3 + -2x + -6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
3 + -2x + -6x2 = 0

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

Divide each side by '-6'.
-0.5 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.3333333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3333333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3333333333x + x2 = 0 + 0.5
0.3333333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.3333333333x + x2 = 0.5

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.5 + 0.02777777779

Combine like terms: 0.5 + 0.02777777779 = 0.52777777779
0.02777777779 + 0.3333333333x + x2 = 0.52777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.52777777779

Calculate the square root of the right side: 0.726483157

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.726483157 and -0.726483157.

Subproblem 1
x + 0.1666666667 = 0.726483157

Simplifying
x + 0.1666666667 = 0.726483157

Reorder the terms:
0.1666666667 + x = 0.726483157

Solving
0.1666666667 + x = 0.726483157

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.726483157 + -0.1666666667
x = 0.726483157 + -0.1666666667

Combine like terms: 0.726483157 + -0.1666666667 = 0.5598164903
x = 0.5598164903

Simplifying
x = 0.5598164903

Subproblem 2
x + 0.1666666667 = -0.726483157

Simplifying
x + 0.1666666667 = -0.726483157

Reorder the terms:
0.1666666667 + x = -0.726483157

Solving
0.1666666667 + x = -0.726483157

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.726483157 + -0.1666666667
x = -0.726483157 + -0.1666666667

Combine like terms: -0.726483157 + -0.1666666667 = -0.8931498237
x = -0.8931498237

Simplifying
x = -0.8931498237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5598164903, -0.8931498237}