(6+2x)(11+2x)=94

Solution for (6+2x)(11+2x)=94 equation:

Simplifying
(6 + 2x)(11 + 2x) = 94

Multiply (6 + 2x) * (11 + 2x)
(6(11 + 2x) + 2x * (11 + 2x)) = 94
((11 * 6 + 2x * 6) + 2x * (11 + 2x)) = 94
((66 + 12x) + 2x * (11 + 2x)) = 94
(66 + 12x + (11 * 2x + 2x * 2x)) = 94
(66 + 12x + (22x + 4x2)) = 94

Combine like terms: 12x + 22x = 34x
(66 + 34x + 4x2) = 94

Solving
66 + 34x + 4x2 = 94

Solving for variable 'x'.

Reorder the terms:
66 + -94 + 34x + 4x2 = 94 + -94

Combine like terms: 66 + -94 = -28
-28 + 34x + 4x2 = 94 + -94

Combine like terms: 94 + -94 = 0
-28 + 34x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 17x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 17x + 2x2)' equal to zero and attempt to solve:

Simplifying
-14 + 17x + 2x2 = 0

Solving
-14 + 17x + 2x2 = 0

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

Divide each side by '2'.
-7 + 8.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 8.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 8.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 8.5x + x2 = 0 + 7
8.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
8.5x + x2 = 7

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 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 7 + 18.0625

Combine like terms: 7 + 18.0625 = 25.0625
18.0625 + 8.5x + x2 = 25.0625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 25.0625

Calculate the square root of the right side: 5.006246099

Break this problem into two subproblems by setting 
(x + 4.25) equal to 5.006246099 and -5.006246099.

Subproblem 1
x + 4.25 = 5.006246099

Simplifying
x + 4.25 = 5.006246099

Reorder the terms:
4.25 + x = 5.006246099

Solving
4.25 + x = 5.006246099

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 = 5.006246099 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 5.006246099 + -4.25
x = 5.006246099 + -4.25

Combine like terms: 5.006246099 + -4.25 = 0.756246099
x = 0.756246099

Simplifying
x = 0.756246099

Subproblem 2
x + 4.25 = -5.006246099

Simplifying
x + 4.25 = -5.006246099

Reorder the terms:
4.25 + x = -5.006246099

Solving
4.25 + x = -5.006246099

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 = -5.006246099 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -5.006246099 + -4.25
x = -5.006246099 + -4.25

Combine like terms: -5.006246099 + -4.25 = -9.256246099
x = -9.256246099

Simplifying
x = -9.256246099

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.756246099, -9.256246099}
Solution
x = {0.756246099, -9.256246099}