-6a^4+6a^3-2a^2=0

Solution for -6a^4+6a^3-2a^2=0 equation:

Simplifying
-6a4 + 6a3 + -2a2 = 0

Reorder the terms:
-2a2 + 6a3 + -6a4 = 0

Solving
-2a2 + 6a3 + -6a4 = 0

Solving for variable 'a'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-1 + 3a + -3a2)' equal to zero and attempt to solve:

Simplifying
-1 + 3a + -3a2 = 0

Solving
-1 + 3a + -3a2 = 0

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

Divide each side by '-3'.
0.3333333333 + -1a + a2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1a + -0.3333333333 + a2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1a + a2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1a + a2 = 0 + -0.3333333333
-1a + a2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1a + a2 = -0.3333333333

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = -0.3333333333 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
0.25 + -1a + a2 = -0.0833333333

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -0.0833333333

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}