6x(x+8)=216

Solution for 6x(x+8)=216 equation:

Simplifying
6x(x + 8) = 216

Reorder the terms:
6x(8 + x) = 216
(8 * 6x + x * 6x) = 216
(48x + 6x2) = 216

Solving
48x + 6x2 = 216

Solving for variable 'x'.

Reorder the terms:
-216 + 48x + 6x2 = 216 + -216

Combine like terms: 216 + -216 = 0
-216 + 48x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-36 + 8x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-36 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 8x + x2 = 0

Solving
-36 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 8x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 8x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 8x + x2 = 0 + 36
8x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
8x + x2 = 36

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 36 + 16

Reorder the terms:
16 + 8x + x2 = 36 + 16

Combine like terms: 36 + 16 = 52
16 + 8x + x2 = 52

Factor a perfect square on the left side:
(x + 4)(x + 4) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 4) equal to 7.211102551 and -7.211102551.

Subproblem 1
x + 4 = 7.211102551

Simplifying
x + 4 = 7.211102551

Reorder the terms:
4 + x = 7.211102551

Solving
4 + x = 7.211102551

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 7.211102551 + -4

Combine like terms: 4 + -4 = 0
0 + x = 7.211102551 + -4
x = 7.211102551 + -4

Combine like terms: 7.211102551 + -4 = 3.211102551
x = 3.211102551

Simplifying
x = 3.211102551

Subproblem 2
x + 4 = -7.211102551

Simplifying
x + 4 = -7.211102551

Reorder the terms:
4 + x = -7.211102551

Solving
4 + x = -7.211102551

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -7.211102551 + -4

Combine like terms: 4 + -4 = 0
0 + x = -7.211102551 + -4
x = -7.211102551 + -4

Combine like terms: -7.211102551 + -4 = -11.211102551
x = -11.211102551

Simplifying
x = -11.211102551

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.211102551, -11.211102551}
Solution
x = {3.211102551, -11.211102551}