9a(3a^2-2a-3)-3a(a-2)=

Solution for 9a(3a^2-2a-3)-3a(a-2)= equation:

Simplifying
9a(3a2 + -2a + -3) + -3a(a + -2) = 0

Reorder the terms:
9a(-3 + -2a + 3a2) + -3a(a + -2) = 0
(-3 * 9a + -2a * 9a + 3a2 * 9a) + -3a(a + -2) = 0
(-27a + -18a2 + 27a3) + -3a(a + -2) = 0

Reorder the terms:
-27a + -18a2 + 27a3 + -3a(-2 + a) = 0
-27a + -18a2 + 27a3 + (-2 * -3a + a * -3a) = 0
-27a + -18a2 + 27a3 + (6a + -3a2) = 0

Reorder the terms:
-27a + 6a + -18a2 + -3a2 + 27a3 = 0

Combine like terms: -27a + 6a = -21a
-21a + -18a2 + -3a2 + 27a3 = 0

Combine like terms: -18a2 + -3a2 = -21a2
-21a + -21a2 + 27a3 = 0

Solving
-21a + -21a2 + 27a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-7 + -7a + 9a2) = 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 '(-7 + -7a + 9a2)' equal to zero and attempt to solve:

Simplifying
-7 + -7a + 9a2 = 0

Solving
-7 + -7a + 9a2 = 0

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

Divide each side by '9'.
-0.7777777778 + -0.7777777778a + a2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -0.7777777778a + 0.7777777778 + a2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -0.7777777778a + a2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -0.7777777778a + a2 = 0 + 0.7777777778
-0.7777777778a + a2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-0.7777777778a + a2 = 0.7777777778

The a term is -0.7777777778a.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778a + 0.1512345679 + a2 = 0.7777777778 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778a + a2 = 0.7777777778 + 0.1512345679

Combine like terms: 0.7777777778 + 0.1512345679 = 0.9290123457
0.1512345679 + -0.7777777778a + a2 = 0.9290123457

Factor a perfect square on the left side:
(a + -0.3888888889)(a + -0.3888888889) = 0.9290123457

Calculate the square root of the right side: 0.963852865

Break this problem into two subproblems by setting 
(a + -0.3888888889) equal to 0.963852865 and -0.963852865.

Subproblem 1
a + -0.3888888889 = 0.963852865

Simplifying
a + -0.3888888889 = 0.963852865

Reorder the terms:
-0.3888888889 + a = 0.963852865

Solving
-0.3888888889 + a = 0.963852865

Solving for variable 'a'.

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

Add '0.3888888889' to each side of the equation.
-0.3888888889 + 0.3888888889 + a = 0.963852865 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + a = 0.963852865 + 0.3888888889
a = 0.963852865 + 0.3888888889

Combine like terms: 0.963852865 + 0.3888888889 = 1.3527417539
a = 1.3527417539

Simplifying
a = 1.3527417539

Subproblem 2
a + -0.3888888889 = -0.963852865

Simplifying
a + -0.3888888889 = -0.963852865

Reorder the terms:
-0.3888888889 + a = -0.963852865

Solving
-0.3888888889 + a = -0.963852865

Solving for variable 'a'.

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

Add '0.3888888889' to each side of the equation.
-0.3888888889 + 0.3888888889 + a = -0.963852865 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + a = -0.963852865 + 0.3888888889
a = -0.963852865 + 0.3888888889

Combine like terms: -0.963852865 + 0.3888888889 = -0.5749639761
a = -0.5749639761

Simplifying
a = -0.5749639761

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.3527417539, -0.5749639761}
Solution
a = {0, 1.3527417539, -0.5749639761}