6-20x+12(x^2)=0

Solution for 6-20x+12(x^2)=0 equation:

Simplifying
6 + -20x + 12(x2) = 0

Solving
6 + -20x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -10x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -10x + 6x2)' equal to zero and attempt to solve:

Simplifying
3 + -10x + 6x2 = 0

Solving
3 + -10x + 6x2 = 0

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

Divide each side by '6'.
0.5 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.666666667x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.666666667x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.666666667x + x2 = 0 + -0.5
-1.666666667x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.666666667x + x2 = -0.5

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.5 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.5 + 0.6944444447

Combine like terms: -0.5 + 0.6944444447 = 0.1944444447
0.6944444447 + -1.666666667x + x2 = 0.1944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.1944444447

Calculate the square root of the right side: 0.440958552

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.440958552 and -0.440958552.

Subproblem 1
x + -0.8333333335 = 0.440958552

Simplifying
x + -0.8333333335 = 0.440958552

Reorder the terms:
-0.8333333335 + x = 0.440958552

Solving
-0.8333333335 + x = 0.440958552

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 0.440958552 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 0.440958552 + 0.8333333335
x = 0.440958552 + 0.8333333335

Combine like terms: 0.440958552 + 0.8333333335 = 1.2742918855
x = 1.2742918855

Simplifying
x = 1.2742918855

Subproblem 2
x + -0.8333333335 = -0.440958552

Simplifying
x + -0.8333333335 = -0.440958552

Reorder the terms:
-0.8333333335 + x = -0.440958552

Solving
-0.8333333335 + x = -0.440958552

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -0.440958552 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -0.440958552 + 0.8333333335
x = -0.440958552 + 0.8333333335

Combine like terms: -0.440958552 + 0.8333333335 = 0.3923747815
x = 0.3923747815

Simplifying
x = 0.3923747815

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2742918855, 0.3923747815}
Solution
x = {1.2742918855, 0.3923747815}