6x+((2x)(2x))=216

Solution for 6x+((2x)(2x))=216 equation:

Simplifying
6x + ((2x)(2x)) = 216

Remove parenthesis around (2x)
6x + (2x(2x)) = 216

Remove parenthesis around (2x)
6x + (2x * 2x) = 216

Reorder the terms for easier multiplication:
6x + (2 * 2x * x) = 216

Multiply 2 * 2
6x + (4x * x) = 216

Multiply x * x
6x + (4x2) = 216

Solving
6x + (4x2) = 216

Solving for variable 'x'.

Reorder the terms:
-216 + 6x + (4x2) = 216 + -216

Combine like terms: 216 + -216 = 0
-216 + 6x + (4x2) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-108 + 3x + (2x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-108 + 3x + (2x2))' equal to zero and attempt to solve:

Simplifying
-108 + 3x + (2x2) = 0

Solving
-108 + 3x + (2x2) = 0

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

Divide each side by '2'.
-54 + 1.5x + x2 = 0

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 1.5x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 1.5x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 1.5x + x2 = 0 + 54
1.5x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
1.5x + x2 = 54

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 = 54 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 54 + 0.5625

Combine like terms: 54 + 0.5625 = 54.5625
0.5625 + 1.5x + x2 = 54.5625

Factor a perfect square on the left side:
((x) + 0.75)((x) + 0.75) = 54.5625

Calculate the square root of the right side: 7.386643351

Break this problem into two subproblems by setting 
((x) + 0.75) equal to 7.386643351 and -7.386643351.

Subproblem 1
(x) + 0.75 = 7.386643351

Simplifying
(x) + 0.75 = 7.386643351
x + 0.75 = 7.386643351

Reorder the terms:
0.75 + x = 7.386643351

Solving
0.75 + x = 7.386643351

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 = 7.386643351 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 7.386643351 + -0.75
x = 7.386643351 + -0.75

Combine like terms: 7.386643351 + -0.75 = 6.636643351
x = 6.636643351

Simplifying
x = 6.636643351

Subproblem 2
(x) + 0.75 = -7.386643351

Simplifying
(x) + 0.75 = -7.386643351
x + 0.75 = -7.386643351

Reorder the terms:
0.75 + x = -7.386643351

Solving
0.75 + x = -7.386643351

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 = -7.386643351 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -7.386643351 + -0.75
x = -7.386643351 + -0.75

Combine like terms: -7.386643351 + -0.75 = -8.136643351
x = -8.136643351

Simplifying
x = -8.136643351

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.636643351, -8.136643351}
Solution
x = {6.636643351, -8.136643351}