-12a^4+9a^3-3a^2=0

Solution for -12a^4+9a^3-3a^2=0 equation:

Simplifying
-12a4 + 9a3 + -3a2 = 0

Reorder the terms:
-3a2 + 9a3 + -12a4 = 0

Solving
-3a2 + 9a3 + -12a4 = 0

Solving for variable 'a'.

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

Ignore the factor 3.
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 + -4a2)' equal to zero and attempt to solve:

Simplifying
-1 + 3a + -4a2 = 0

Solving
-1 + 3a + -4a2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -0.75a + a2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.75a + -0.25 + a2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.75a + a2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.75a + a2 = 0 + -0.25
-0.75a + a2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.75a + a2 = -0.25

The a term is -0.75a.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75a + 0.140625 + a2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + -0.75a + a2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + -0.75a + a2 = -0.109375

Factor a perfect square on the left side:
(a + -0.375)(a + -0.375) = -0.109375

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}