12a^3-24a^2+4a=

Solution for 12a^3-24a^2+4a= equation:

Simplifying
12a3 + -24a2 + 4a = 0

Reorder the terms:
4a + -24a2 + 12a3 = 0

Solving
4a + -24a2 + 12a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(1 + -6a + 3a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + -6a + 3a2)' equal to zero and attempt to solve:

Simplifying
1 + -6a + 3a2 = 0

Solving
1 + -6a + 3a2 = 0

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

Divide each side by '3'.
0.3333333333 + -2a + a2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2a + -0.3333333333 + a2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2a + a2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2a + a2 = 0 + -0.3333333333
-2a + a2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2a + a2 = -0.3333333333

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -0.3333333333 + 1

Reorder the terms:
1 + -2a + a2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2a + a2 = 0.6666666667

Factor a perfect square on the left side:
(a + -1)(a + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(a + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1
a + -1 = 0.816496581

Simplifying
a + -1 = 0.816496581

Reorder the terms:
-1 + a = 0.816496581

Solving
-1 + a = 0.816496581

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + a = 0.816496581 + 1
a = 0.816496581 + 1

Combine like terms: 0.816496581 + 1 = 1.816496581
a = 1.816496581

Simplifying
a = 1.816496581

Subproblem 2
a + -1 = -0.816496581

Simplifying
a + -1 = -0.816496581

Reorder the terms:
-1 + a = -0.816496581

Solving
-1 + a = -0.816496581

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + a = -0.816496581 + 1
a = -0.816496581 + 1

Combine like terms: -0.816496581 + 1 = 0.183503419
a = 0.183503419

Simplifying
a = 0.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.816496581, 0.183503419}
Solution
a = {0, 1.816496581, 0.183503419}