-4a^2(3a^2-4a+3)=0

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

Simplifying
-4a2(3a2 + -4a + 3) = 0

Reorder the terms:
-4a2(3 + -4a + 3a2) = 0
(3 * -4a2 + -4a * -4a2 + 3a2 * -4a2) = 0
(-12a2 + 16a3 + -12a4) = 0

Solving
-12a2 + 16a3 + -12a4 = 0

Solving for variable 'a'.

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

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

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

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

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

Divide each side by '-3'.
1 + -1.333333333a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.333333333a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + -1.333333333a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.333333333a + a2 = 0 + -1
-1.333333333a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.333333333a + a2 = -1

The a term is -1.333333333a.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333a + 0.4444444442 + a2 = -1 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333a + a2 = -1 + 0.4444444442

Combine like terms: -1 + 0.4444444442 = -0.5555555558
0.4444444442 + -1.333333333a + a2 = -0.5555555558

Factor a perfect square on the left side:
(a + -0.6666666665)(a + -0.6666666665) = -0.5555555558

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}