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

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

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

Reorder the terms:
2x(-5 + -1x) = 6 + (x + 1)
(-5 * 2x + -1x * 2x) = 6 + (x + 1)
(-10x + -2x2) = 6 + (x + 1)

Reorder the terms:
-10x + -2x2 = 6 + (1 + x)

Remove parenthesis around (1 + x)
-10x + -2x2 = 6 + 1 + x

Combine like terms: 6 + 1 = 7
-10x + -2x2 = 7 + x

Solving
-10x + -2x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-7 + -10x + -1x + -2x2 = 7 + x + -7 + -1x

Combine like terms: -10x + -1x = -11x
-7 + -11x + -2x2 = 7 + x + -7 + -1x

Reorder the terms:
-7 + -11x + -2x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-7 + -11x + -2x2 = 0 + x + -1x
-7 + -11x + -2x2 = x + -1x

Combine like terms: x + -1x = 0
-7 + -11x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 11x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + 11x + 2x2 = 0

Solving
7 + 11x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 5.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 5.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 5.5x + x2 = 0 + -3.5
5.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
5.5x + x2 = -3.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -3.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -3.5 + 7.5625

Combine like terms: -3.5 + 7.5625 = 4.0625
7.5625 + 5.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.015564437 and -2.015564437.

Subproblem 1
x + 2.75 = 2.015564437

Simplifying
x + 2.75 = 2.015564437

Reorder the terms:
2.75 + x = 2.015564437

Solving
2.75 + x = 2.015564437

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 2.015564437 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 2.015564437 + -2.75
x = 2.015564437 + -2.75

Combine like terms: 2.015564437 + -2.75 = -0.734435563
x = -0.734435563

Simplifying
x = -0.734435563

Subproblem 2
x + 2.75 = -2.015564437

Simplifying
x + 2.75 = -2.015564437

Reorder the terms:
2.75 + x = -2.015564437

Solving
2.75 + x = -2.015564437

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -2.015564437 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -2.015564437 + -2.75
x = -2.015564437 + -2.75

Combine like terms: -2.015564437 + -2.75 = -4.765564437
x = -4.765564437

Simplifying
x = -4.765564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.734435563, -4.765564437}
Solution
x = {-0.734435563, -4.765564437}