3x(2x+6)=8

Solution for 3x(2x+6)=8 equation:

Simplifying
3x(2x + 6) = 8

Reorder the terms:
3x(6 + 2x) = 8
(6 * 3x + 2x * 3x) = 8
(18x + 6x2) = 8

Solving
18x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 18x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 18x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 9x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 9x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 9x + 3x2 = 0

Solving
-4 + 9x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 3x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 3x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 3x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + 1.333333333
3x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
3x + x2 = 1.333333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1.333333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.333333333 + 2.25

Combine like terms: 1.333333333 + 2.25 = 3.583333333
2.25 + 3x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.892969449 and -1.892969449.

Subproblem 1
x + 1.5 = 1.892969449

Simplifying
x + 1.5 = 1.892969449

Reorder the terms:
1.5 + x = 1.892969449

Solving
1.5 + x = 1.892969449

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.892969449 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.892969449 + -1.5
x = 1.892969449 + -1.5

Combine like terms: 1.892969449 + -1.5 = 0.392969449
x = 0.392969449

Simplifying
x = 0.392969449

Subproblem 2
x + 1.5 = -1.892969449

Simplifying
x + 1.5 = -1.892969449

Reorder the terms:
1.5 + x = -1.892969449

Solving
1.5 + x = -1.892969449

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.892969449 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.892969449 + -1.5
x = -1.892969449 + -1.5

Combine like terms: -1.892969449 + -1.5 = -3.392969449
x = -3.392969449

Simplifying
x = -3.392969449

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.392969449, -3.392969449}
Solution
x = {0.392969449, -3.392969449}