-3a(4a^2-5a+9)=0

Solution for -3a(4a^2-5a+9)=0 equation:

Simplifying
-3a(4a2 + -5a + 9) = 0

Reorder the terms:
-3a(9 + -5a + 4a2) = 0
(9 * -3a + -5a * -3a + 4a2 * -3a) = 0
(-27a + 15a2 + -12a3) = 0

Solving
-27a + 15a2 + -12a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-9 + 5a + -4a2) = 0

Ignore the factor 3.
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 '(-9 + 5a + -4a2)' equal to zero and attempt to solve:

Simplifying
-9 + 5a + -4a2 = 0

Solving
-9 + 5a + -4a2 = 0

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

Divide each side by '-4'.
2.25 + -1.25a + a2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -1.25a + -2.25 + a2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -1.25a + a2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -1.25a + a2 = 0 + -2.25
-1.25a + a2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-1.25a + a2 = -2.25

The a term is -1.25a.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25a + 0.390625 + a2 = -2.25 + 0.390625

Reorder the terms:
0.390625 + -1.25a + a2 = -2.25 + 0.390625

Combine like terms: -2.25 + 0.390625 = -1.859375
0.390625 + -1.25a + a2 = -1.859375

Factor a perfect square on the left side:
(a + -0.625)(a + -0.625) = -1.859375

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}