12x+6-3=6x^2

Solution for 12x+6-3=6x^2 equation:

Simplifying
12x + 6 + -3 = 6x2

Reorder the terms:
6 + -3 + 12x = 6x2

Combine like terms: 6 + -3 = 3
3 + 12x = 6x2

Solving
3 + 12x = 6x2

Solving for variable 'x'.

Combine like terms: 6x2 + -6x2 = 0
3 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4x + -2x2) = 0

Ignore the factor 3.
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 = 1.5
1 + -2x + x2 = 1.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1
x + -1 = 1.224744871

Simplifying
x + -1 = 1.224744871

Reorder the terms:
-1 + x = 1.224744871

Solving
-1 + x = 1.224744871

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 = 1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.224744871 + 1
x = 1.224744871 + 1

Combine like terms: 1.224744871 + 1 = 2.224744871
x = 2.224744871

Simplifying
x = 2.224744871

Subproblem 2
x + -1 = -1.224744871

Simplifying
x + -1 = -1.224744871

Reorder the terms:
-1 + x = -1.224744871

Solving
-1 + x = -1.224744871

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 = -1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.224744871 + 1
x = -1.224744871 + 1

Combine like terms: -1.224744871 + 1 = -0.224744871
x = -0.224744871

Simplifying
x = -0.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.224744871, -0.224744871}
Solution
x = {2.224744871, -0.224744871}