(8x+56)(x+11)=10

Solution for (8x+56)(x+11)=10 equation:

Simplifying
(8x + 56)(x + 11) = 10

Reorder the terms:
(56 + 8x)(x + 11) = 10

Reorder the terms:
(56 + 8x)(11 + x) = 10

Multiply (56 + 8x) * (11 + x)
(56(11 + x) + 8x * (11 + x)) = 10
((11 * 56 + x * 56) + 8x * (11 + x)) = 10
((616 + 56x) + 8x * (11 + x)) = 10
(616 + 56x + (11 * 8x + x * 8x)) = 10
(616 + 56x + (88x + 8x2)) = 10

Combine like terms: 56x + 88x = 144x
(616 + 144x + 8x2) = 10

Solving
616 + 144x + 8x2 = 10

Solving for variable 'x'.

Reorder the terms:
616 + -10 + 144x + 8x2 = 10 + -10

Combine like terms: 616 + -10 = 606
606 + 144x + 8x2 = 10 + -10

Combine like terms: 10 + -10 = 0
606 + 144x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(303 + 72x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(303 + 72x + 4x2)' equal to zero and attempt to solve:

Simplifying
303 + 72x + 4x2 = 0

Solving
303 + 72x + 4x2 = 0

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

Divide each side by '4'.
75.75 + 18x + x2 = 0

Move the constant term to the right:

Add '-75.75' to each side of the equation.
75.75 + 18x + -75.75 + x2 = 0 + -75.75

Reorder the terms:
75.75 + -75.75 + 18x + x2 = 0 + -75.75

Combine like terms: 75.75 + -75.75 = 0.00
0.00 + 18x + x2 = 0 + -75.75
18x + x2 = 0 + -75.75

Combine like terms: 0 + -75.75 = -75.75
18x + x2 = -75.75

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -75.75 + 81

Reorder the terms:
81 + 18x + x2 = -75.75 + 81

Combine like terms: -75.75 + 81 = 5.25
81 + 18x + x2 = 5.25

Factor a perfect square on the left side:
(x + 9)(x + 9) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 9) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + 9 = 2.291287847

Simplifying
x + 9 = 2.291287847

Reorder the terms:
9 + x = 2.291287847

Solving
9 + x = 2.291287847

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 2.291287847 + -9

Combine like terms: 9 + -9 = 0
0 + x = 2.291287847 + -9
x = 2.291287847 + -9

Combine like terms: 2.291287847 + -9 = -6.708712153
x = -6.708712153

Simplifying
x = -6.708712153

Subproblem 2
x + 9 = -2.291287847

Simplifying
x + 9 = -2.291287847

Reorder the terms:
9 + x = -2.291287847

Solving
9 + x = -2.291287847

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -2.291287847 + -9

Combine like terms: 9 + -9 = 0
0 + x = -2.291287847 + -9
x = -2.291287847 + -9

Combine like terms: -2.291287847 + -9 = -11.291287847
x = -11.291287847

Simplifying
x = -11.291287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.708712153, -11.291287847}
Solution
x = {-6.708712153, -11.291287847}