12x^3-4x^2=2x

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Solution for 12x^3-4x^2=2x equation: 


Simplifying
12x3 + -4x2 = 2x

Reorder the terms:
-4x2 + 12x3 = 2x

Solving
-4x2 + 12x3 = 2x

Solving for variable 'x'.

Reorder the terms:
-2x + -4x2 + 12x3 = 2x + -2x

Combine like terms: 2x + -2x = 0
-2x + -4x2 + 12x3 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-1 + -2x + 6x2 = 0

Solving
-1 + -2x + 6x2 = 0

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

Divide each side by '6'.
-0.1666666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.3333333333x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.3333333333x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.3333333333x + x2 = 0 + 0.1666666667
-0.3333333333x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.3333333333x + x2 = 0.1666666667

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.1666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.1666666667 + 0.02777777779

Combine like terms: 0.1666666667 + 0.02777777779 = 0.19444444449
0.02777777779 + -0.3333333333x + x2 = 0.19444444449

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 0.19444444449

Calculate the square root of the right side: 0.440958552

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 0.440958552 and -0.440958552.


Subproblem 1
x + -0.1666666667 = 0.440958552

Simplifying
x + -0.1666666667 = 0.440958552

Reorder the terms:
-0.1666666667 + x = 0.440958552

Solving
-0.1666666667 + x = 0.440958552

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 0.440958552 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 0.440958552 + 0.1666666667
x = 0.440958552 + 0.1666666667

Combine like terms: 0.440958552 + 0.1666666667 = 0.6076252187
x = 0.6076252187

Simplifying
x = 0.6076252187


Subproblem 2
x + -0.1666666667 = -0.440958552

Simplifying
x + -0.1666666667 = -0.440958552

Reorder the terms:
-0.1666666667 + x = -0.440958552

Solving
-0.1666666667 + x = -0.440958552

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -0.440958552 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -0.440958552 + 0.1666666667
x = -0.440958552 + 0.1666666667

Combine like terms: -0.440958552 + 0.1666666667 = -0.2742918853
x = -0.2742918853

Simplifying
x = -0.2742918853


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6076252187, -0.2742918853}
Solution
x = {0, 0.6076252187, -0.2742918853}

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