6a^3-12a^2+14a=

Solution for 6a^3-12a^2+14a= equation:

Simplifying
6a3 + -12a2 + 14a = 0

Reorder the terms:
14a + -12a2 + 6a3 = 0

Solving
14a + -12a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(7 + -6a + 3a2) = 0

Ignore the factor 2.
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 '(7 + -6a + 3a2)' equal to zero and attempt to solve:

Simplifying
7 + -6a + 3a2 = 0

Solving
7 + -6a + 3a2 = 0

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

Divide each side by '3'.
2.333333333 + -2a + a2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -2a + -2.333333333 + a2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -2a + a2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -2a + a2 = 0 + -2.333333333
-2a + a2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-2a + a2 = -2.333333333

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 = -2.333333333 + 1

Reorder the terms:
1 + -2a + a2 = -2.333333333 + 1

Combine like terms: -2.333333333 + 1 = -1.333333333
1 + -2a + a2 = -1.333333333

Factor a perfect square on the left side:
(a + -1)(a + -1) = -1.333333333

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}