(11+2x)(6+2x)-66=30

Solution for (11+2x)(6+2x)-66=30 equation:

Simplifying
(11 + 2x)(6 + 2x) + -66 = 30

Multiply (11 + 2x) * (6 + 2x)
(11(6 + 2x) + 2x * (6 + 2x)) + -66 = 30
((6 * 11 + 2x * 11) + 2x * (6 + 2x)) + -66 = 30
((66 + 22x) + 2x * (6 + 2x)) + -66 = 30
(66 + 22x + (6 * 2x + 2x * 2x)) + -66 = 30
(66 + 22x + (12x + 4x2)) + -66 = 30

Combine like terms: 22x + 12x = 34x
(66 + 34x + 4x2) + -66 = 30

Reorder the terms:
66 + -66 + 34x + 4x2 = 30

Combine like terms: 66 + -66 = 0
0 + 34x + 4x2 = 30
34x + 4x2 = 30

Solving
34x + 4x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 34x + 4x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 34x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 17x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 17x + 2x2)' equal to zero and attempt to solve:

Simplifying
-15 + 17x + 2x2 = 0

Solving
-15 + 17x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + 8.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 8.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 8.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 8.5x + x2 = 0 + 7.5
8.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
8.5x + x2 = 7.5

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 7.5 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 7.5 + 18.0625

Combine like terms: 7.5 + 18.0625 = 25.5625
18.0625 + 8.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + 4.25) equal to 5.055937104 and -5.055937104.

Subproblem 1
x + 4.25 = 5.055937104

Simplifying
x + 4.25 = 5.055937104

Reorder the terms:
4.25 + x = 5.055937104

Solving
4.25 + x = 5.055937104

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 5.055937104 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 5.055937104 + -4.25
x = 5.055937104 + -4.25

Combine like terms: 5.055937104 + -4.25 = 0.805937104
x = 0.805937104

Simplifying
x = 0.805937104

Subproblem 2
x + 4.25 = -5.055937104

Simplifying
x + 4.25 = -5.055937104

Reorder the terms:
4.25 + x = -5.055937104

Solving
4.25 + x = -5.055937104

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -5.055937104 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -5.055937104 + -4.25
x = -5.055937104 + -4.25

Combine like terms: -5.055937104 + -4.25 = -9.305937104
x = -9.305937104

Simplifying
x = -9.305937104

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.805937104, -9.305937104}
Solution
x = {0.805937104, -9.305937104}