-8x(x+1)=4(x-11)

Solution for -8x(x+1)=4(x-11) equation:

Simplifying
-8x(x + 1) = 4(x + -11)

Reorder the terms:
-8x(1 + x) = 4(x + -11)
(1 * -8x + x * -8x) = 4(x + -11)
(-8x + -8x2) = 4(x + -11)

Reorder the terms:
-8x + -8x2 = 4(-11 + x)
-8x + -8x2 = (-11 * 4 + x * 4)
-8x + -8x2 = (-44 + 4x)

Solving
-8x + -8x2 = -44 + 4x

Solving for variable 'x'.

Reorder the terms:
44 + -8x + -4x + -8x2 = -44 + 4x + 44 + -4x

Combine like terms: -8x + -4x = -12x
44 + -12x + -8x2 = -44 + 4x + 44 + -4x

Reorder the terms:
44 + -12x + -8x2 = -44 + 44 + 4x + -4x

Combine like terms: -44 + 44 = 0
44 + -12x + -8x2 = 0 + 4x + -4x
44 + -12x + -8x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
44 + -12x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(11 + -3x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(11 + -3x + -2x2)' equal to zero and attempt to solve:

Simplifying
11 + -3x + -2x2 = 0

Solving
11 + -3x + -2x2 = 0

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

Divide each side by '-2'.
-5.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 1.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 1.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 1.5x + x2 = 0 + 5.5
1.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
1.5x + x2 = 5.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 5.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 5.5 + 0.5625

Combine like terms: 5.5 + 0.5625 = 6.0625
0.5625 + 1.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.46221445 and -2.46221445.

Subproblem 1
x + 0.75 = 2.46221445

Simplifying
x + 0.75 = 2.46221445

Reorder the terms:
0.75 + x = 2.46221445

Solving
0.75 + x = 2.46221445

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.46221445 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.46221445 + -0.75
x = 2.46221445 + -0.75

Combine like terms: 2.46221445 + -0.75 = 1.71221445
x = 1.71221445

Simplifying
x = 1.71221445

Subproblem 2
x + 0.75 = -2.46221445

Simplifying
x + 0.75 = -2.46221445

Reorder the terms:
0.75 + x = -2.46221445

Solving
0.75 + x = -2.46221445

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.46221445 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.46221445 + -0.75
x = -2.46221445 + -0.75

Combine like terms: -2.46221445 + -0.75 = -3.21221445
x = -3.21221445

Simplifying
x = -3.21221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.71221445, -3.21221445}
Solution
x = {1.71221445, -3.21221445}