12x^2+24x-2=0

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

Simplifying
12x2 + 24x + -2 = 0

Reorder the terms:
-2 + 24x + 12x2 = 0

Solving
-2 + 24x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 12x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 12x + 6x2)' equal to zero and attempt to solve:

Simplifying
-1 + 12x + 6x2 = 0

Solving
-1 + 12x + 6x2 = 0

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

Divide each side by '6'.
-0.1666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 2x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 2x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + 0.1666666667
2x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
2x + x2 = 0.1666666667

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 = 0.1666666667 + 1

Reorder the terms:
1 + 2x + x2 = 0.1666666667 + 1

Combine like terms: 0.1666666667 + 1 = 1.1666666667
1 + 2x + x2 = 1.1666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.1666666667

Calculate the square root of the right side: 1.08012345

Break this problem into two subproblems by setting 
(x + 1) equal to 1.08012345 and -1.08012345.

Subproblem 1
x + 1 = 1.08012345

Simplifying
x + 1 = 1.08012345

Reorder the terms:
1 + x = 1.08012345

Solving
1 + x = 1.08012345

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 = 1.08012345 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.08012345 + -1
x = 1.08012345 + -1

Combine like terms: 1.08012345 + -1 = 0.08012345
x = 0.08012345

Simplifying
x = 0.08012345

Subproblem 2
x + 1 = -1.08012345

Simplifying
x + 1 = -1.08012345

Reorder the terms:
1 + x = -1.08012345

Solving
1 + x = -1.08012345

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 = -1.08012345 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.08012345 + -1
x = -1.08012345 + -1

Combine like terms: -1.08012345 + -1 = -2.08012345
x = -2.08012345

Simplifying
x = -2.08012345

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.08012345, -2.08012345}
Solution
x = {0.08012345, -2.08012345}