x^2-0.427157255525x^2-6x+4*-0.427157255525x+4*2=12

Solution for x^2-0.427157255525x^2-6x+4*-0.427157255525x+4*2=12 equation:

Simplifying
x2 + -0.427157255525x2 + -6x + 4 * -0.427157255525x + 4 * 2 = 12

Multiply 4 * -0.427157255525
x2 + -0.427157255525x2 + -6x + -1.708629022x + 4 * 2 = 12

Multiply 4 * 2
x2 + -0.427157255525x2 + -6x + -1.708629022x + 8 = 12

Reorder the terms:
8 + -6x + -1.708629022x + x2 + -0.427157255525x2 = 12

Combine like terms: -6x + -1.708629022x = -7.708629022x
8 + -7.708629022x + x2 + -0.427157255525x2 = 12

Combine like terms: x2 + -0.427157255525x2 = 0.572842744475x2
8 + -7.708629022x + 0.572842744475x2 = 12

Solving
8 + -7.708629022x + 0.572842744475x2 = 12

Solving for variable 'x'.

Reorder the terms:
8 + -12 + -7.708629022x + 0.572842744475x2 = 12 + -12

Combine like terms: 8 + -12 = -4
-4 + -7.708629022x + 0.572842744475x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-4 + -7.708629022x + 0.572842744475x2 = 0

Begin completing the square.  Divide all terms by
0.572842744475 the coefficient of the squared term: 

Divide each side by '0.572842744475'.
-6.982719147 + -13.45679787x + x2 = 0

Move the constant term to the right:

Add '6.982719147' to each side of the equation.
-6.982719147 + -13.45679787x + 6.982719147 + x2 = 0 + 6.982719147

Reorder the terms:
-6.982719147 + 6.982719147 + -13.45679787x + x2 = 0 + 6.982719147

Combine like terms: -6.982719147 + 6.982719147 = 0.000000000
0.000000000 + -13.45679787x + x2 = 0 + 6.982719147
-13.45679787x + x2 = 0 + 6.982719147

Combine like terms: 0 + 6.982719147 = 6.982719147
-13.45679787x + x2 = 6.982719147

The x term is -13.45679787x.  Take half its coefficient (-6.728398935).
Square it (45.27135223) and add it to both sides.

Add '45.27135223' to each side of the equation.
-13.45679787x + 45.27135223 + x2 = 6.982719147 + 45.27135223

Reorder the terms:
45.27135223 + -13.45679787x + x2 = 6.982719147 + 45.27135223

Combine like terms: 6.982719147 + 45.27135223 = 52.254071377
45.27135223 + -13.45679787x + x2 = 52.254071377

Factor a perfect square on the left side:
(x + -6.728398935)(x + -6.728398935) = 52.254071377

Calculate the square root of the right side: 7.228697765

Break this problem into two subproblems by setting 
(x + -6.728398935) equal to 7.228697765 and -7.228697765.

Subproblem 1
x + -6.728398935 = 7.228697765

Simplifying
x + -6.728398935 = 7.228697765

Reorder the terms:
-6.728398935 + x = 7.228697765

Solving
-6.728398935 + x = 7.228697765

Solving for variable 'x'.

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

Add '6.728398935' to each side of the equation.
-6.728398935 + 6.728398935 + x = 7.228697765 + 6.728398935

Combine like terms: -6.728398935 + 6.728398935 = 0.000000000
0.000000000 + x = 7.228697765 + 6.728398935
x = 7.228697765 + 6.728398935

Combine like terms: 7.228697765 + 6.728398935 = 13.9570967
x = 13.9570967

Simplifying
x = 13.9570967

Subproblem 2
x + -6.728398935 = -7.228697765

Simplifying
x + -6.728398935 = -7.228697765

Reorder the terms:
-6.728398935 + x = -7.228697765

Solving
-6.728398935 + x = -7.228697765

Solving for variable 'x'.

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

Add '6.728398935' to each side of the equation.
-6.728398935 + 6.728398935 + x = -7.228697765 + 6.728398935

Combine like terms: -6.728398935 + 6.728398935 = 0.000000000
0.000000000 + x = -7.228697765 + 6.728398935
x = -7.228697765 + 6.728398935

Combine like terms: -7.228697765 + 6.728398935 = -0.50029883
x = -0.50029883

Simplifying
x = -0.50029883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.9570967, -0.50029883}