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)
-10x + -2x2 = (1 * 6 + x * 6)
-10x + -2x2 = (6 + 6x)

Solving
-10x + -2x2 = 6 + 6x

Solving for variable 'x'.

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

Combine like terms: -10x + -6x = -16x
-6 + -16x + -2x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-6 + -16x + -2x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-6 + -16x + -2x2 = 0 + 6x + -6x
-6 + -16x + -2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + -16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 8x + x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 8x + x2 = 0

Solving
3 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 8x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 8x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x + x2 = 0 + -3
8x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
8x + x2 = -3

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -3 + 16

Reorder the terms:
16 + 8x + x2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + 8x + x2 = 13

Factor a perfect square on the left side:
(x + 4)(x + 4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 4) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + 4 = 3.605551275

Simplifying
x + 4 = 3.605551275

Reorder the terms:
4 + x = 3.605551275

Solving
4 + x = 3.605551275

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.605551275 + -4
x = 3.605551275 + -4

Combine like terms: 3.605551275 + -4 = -0.394448725
x = -0.394448725

Simplifying
x = -0.394448725

Subproblem 2
x + 4 = -3.605551275

Simplifying
x + 4 = -3.605551275

Reorder the terms:
4 + x = -3.605551275

Solving
4 + x = -3.605551275

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.605551275 + -4
x = -3.605551275 + -4

Combine like terms: -3.605551275 + -4 = -7.605551275
x = -7.605551275

Simplifying
x = -7.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.394448725, -7.605551275}
Solution
x = {-0.394448725, -7.605551275}