0=12x^2+24x+6

Solution for 0=12x^2+24x+6 equation:

Simplifying
0 = 12x2 + 24x + 6

Reorder the terms:
0 = 6 + 24x + 12x2

Solving
0 = 6 + 24x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -24x + -12x2 = 6 + 24x + 12x2 + -6 + -24x + -12x2

Reorder the terms:
-6 + -24x + -12x2 = 6 + -6 + 24x + -24x + 12x2 + -12x2

Combine like terms: 6 + -6 = 0
-6 + -24x + -12x2 = 0 + 24x + -24x + 12x2 + -12x2
-6 + -24x + -12x2 = 24x + -24x + 12x2 + -12x2

Combine like terms: 24x + -24x = 0
-6 + -24x + -12x2 = 0 + 12x2 + -12x2
-6 + -24x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-6 + -24x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(1 + 4x + 2x2) = 0

Ignore the factor -6.
Subproblem 1
Set the factor '(1 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 4x + 2x2 = 0

Solving
1 + 4x + 2x2 = 0

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

Divide each side by '2'.
0.5 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2x + x2 = 0 + -0.5
2x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2x + x2 = -0.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.5 + 1

Reorder the terms:
1 + 2x + x2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + 2x + x2 = 0.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 1) equal to 0.707106781 and -0.707106781.

Subproblem 1
x + 1 = 0.707106781

Simplifying
x + 1 = 0.707106781

Reorder the terms:
1 + x = 0.707106781

Solving
1 + x = 0.707106781

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.707106781 + -1
x = 0.707106781 + -1

Combine like terms: 0.707106781 + -1 = -0.292893219
x = -0.292893219

Simplifying
x = -0.292893219

Subproblem 2
x + 1 = -0.707106781

Simplifying
x + 1 = -0.707106781

Reorder the terms:
1 + x = -0.707106781

Solving
1 + x = -0.707106781

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.707106781 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.707106781 + -1
x = -0.707106781 + -1

Combine like terms: -0.707106781 + -1 = -1.707106781
x = -1.707106781

Simplifying
x = -1.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.292893219, -1.707106781}
Solution
x = {-0.292893219, -1.707106781}