12a^3-6a^2+18a=

Solution for 12a^3-6a^2+18a= equation:

Simplifying
12a3 + -6a2 + 18a = 0

Reorder the terms:
18a + -6a2 + 12a3 = 0

Solving
18a + -6a2 + 12a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6a'.
6a(3 + -1a + 2a2) = 0

Ignore the factor 6.
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 '(3 + -1a + 2a2)' equal to zero and attempt to solve:

Simplifying
3 + -1a + 2a2 = 0

Solving
3 + -1a + 2a2 = 0

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

Divide each side by '2'.
1.5 + -0.5a + a2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5a + -1.5 + a2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5a + a2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5a + a2 = 0 + -1.5
-0.5a + a2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5a + a2 = -1.5

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = -1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + -0.5a + a2 = -1.4375

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}