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

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

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

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

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

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

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

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

Combine like terms: -2 + 5 = 3
6 + -8x + -6x2 = 3 + -5x + -2x

Combine like terms: -5x + -2x = -7x
6 + -8x + -6x2 = 3 + -7x

Solving
6 + -8x + -6x2 = 3 + -7x

Solving for variable 'x'.

Reorder the terms:
6 + -3 + -8x + 7x + -6x2 = 3 + -7x + -3 + 7x

Combine like terms: 6 + -3 = 3
3 + -8x + 7x + -6x2 = 3 + -7x + -3 + 7x

Combine like terms: -8x + 7x = -1x
3 + -1x + -6x2 = 3 + -7x + -3 + 7x

Reorder the terms:
3 + -1x + -6x2 = 3 + -3 + -7x + 7x

Combine like terms: 3 + -3 = 0
3 + -1x + -6x2 = 0 + -7x + 7x
3 + -1x + -6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
3 + -1x + -6x2 = 0

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

Divide each side by '-6'.
-0.5 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.1666666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.1666666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.1666666667x + x2 = 0 + 0.5
0.1666666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.1666666667x + x2 = 0.5

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 0.5 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 0.5 + 0.006944444447

Combine like terms: 0.5 + 0.006944444447 = 0.506944444447
0.006944444447 + 0.1666666667x + x2 = 0.506944444447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 0.506944444447

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 0.712000312 and -0.712000312.

Subproblem 1
x + 0.08333333335 = 0.712000312

Simplifying
x + 0.08333333335 = 0.712000312

Reorder the terms:
0.08333333335 + x = 0.712000312

Solving
0.08333333335 + x = 0.712000312

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 0.712000312 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 0.712000312 + -0.08333333335
x = 0.712000312 + -0.08333333335

Combine like terms: 0.712000312 + -0.08333333335 = 0.62866697865
x = 0.62866697865

Simplifying
x = 0.62866697865

Subproblem 2
x + 0.08333333335 = -0.712000312

Simplifying
x + 0.08333333335 = -0.712000312

Reorder the terms:
0.08333333335 + x = -0.712000312

Solving
0.08333333335 + x = -0.712000312

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -0.712000312 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -0.712000312 + -0.08333333335
x = -0.712000312 + -0.08333333335

Combine like terms: -0.712000312 + -0.08333333335 = -0.79533364535
x = -0.79533364535

Simplifying
x = -0.79533364535

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.62866697865, -0.79533364535}