11(x-3)(4+2x)=11

Solution for 11(x-3)(4+2x)=11 equation:

Simplifying
11(x + -3)(4 + 2x) = 11

Reorder the terms:
11(-3 + x)(4 + 2x) = 11

Multiply (-3 + x) * (4 + 2x)
11(-3(4 + 2x) + x(4 + 2x)) = 11
11((4 * -3 + 2x * -3) + x(4 + 2x)) = 11
11((-12 + -6x) + x(4 + 2x)) = 11
11(-12 + -6x + (4 * x + 2x * x)) = 11
11(-12 + -6x + (4x + 2x2)) = 11

Combine like terms: -6x + 4x = -2x
11(-12 + -2x + 2x2) = 11
(-12 * 11 + -2x * 11 + 2x2 * 11) = 11
(-132 + -22x + 22x2) = 11

Solving
-132 + -22x + 22x2 = 11

Solving for variable 'x'.

Reorder the terms:
-132 + -11 + -22x + 22x2 = 11 + -11

Combine like terms: -132 + -11 = -143
-143 + -22x + 22x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-143 + -22x + 22x2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(-13 + -2x + 2x2) = 0

Ignore the factor 11.
Subproblem 1
Set the factor '(-13 + -2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-13 + -2x + 2x2 = 0

Solving
-13 + -2x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + -1x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -1x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -1x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -1x + x2 = 0 + 6.5
-1x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-1x + x2 = 6.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 6.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 6.5 + 0.25

Combine like terms: 6.5 + 0.25 = 6.75
0.25 + -1x + x2 = 6.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.598076211 and -2.598076211.

Subproblem 1
x + -0.5 = 2.598076211

Simplifying
x + -0.5 = 2.598076211

Reorder the terms:
-0.5 + x = 2.598076211

Solving
-0.5 + x = 2.598076211

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.598076211 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.598076211 + 0.5
x = 2.598076211 + 0.5

Combine like terms: 2.598076211 + 0.5 = 3.098076211
x = 3.098076211

Simplifying
x = 3.098076211

Subproblem 2
x + -0.5 = -2.598076211

Simplifying
x + -0.5 = -2.598076211

Reorder the terms:
-0.5 + x = -2.598076211

Solving
-0.5 + x = -2.598076211

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.598076211 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.598076211 + 0.5
x = -2.598076211 + 0.5

Combine like terms: -2.598076211 + 0.5 = -2.098076211
x = -2.098076211

Simplifying
x = -2.098076211

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.098076211, -2.098076211}
Solution
x = {3.098076211, -2.098076211}