8a(3a^2-5a-3)-4a(a-2)=0

Solution for 8a(3a^2-5a-3)-4a(a-2)=0 equation:

Simplifying
8a(3a2 + -5a + -3) + -4a(a + -2) = 0

Reorder the terms:
8a(-3 + -5a + 3a2) + -4a(a + -2) = 0
(-3 * 8a + -5a * 8a + 3a2 * 8a) + -4a(a + -2) = 0
(-24a + -40a2 + 24a3) + -4a(a + -2) = 0

Reorder the terms:
-24a + -40a2 + 24a3 + -4a(-2 + a) = 0
-24a + -40a2 + 24a3 + (-2 * -4a + a * -4a) = 0
-24a + -40a2 + 24a3 + (8a + -4a2) = 0

Reorder the terms:
-24a + 8a + -40a2 + -4a2 + 24a3 = 0

Combine like terms: -24a + 8a = -16a
-16a + -40a2 + -4a2 + 24a3 = 0

Combine like terms: -40a2 + -4a2 = -44a2
-16a + -44a2 + 24a3 = 0

Solving
-16a + -44a2 + 24a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-4 + -11a + 6a2) = 0

Ignore the factor 4.
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 '(-4 + -11a + 6a2)' equal to zero and attempt to solve:

Simplifying
-4 + -11a + 6a2 = 0

Solving
-4 + -11a + 6a2 = 0

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

Divide each side by '6'.
-0.6666666667 + -1.833333333a + a2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1.833333333a + 0.6666666667 + a2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1.833333333a + a2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1.833333333a + a2 = 0 + 0.6666666667
-1.833333333a + a2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1.833333333a + a2 = 0.6666666667

The a term is -1.833333333a.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333a + 0.8402777775 + a2 = 0.6666666667 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333a + a2 = 0.6666666667 + 0.8402777775

Combine like terms: 0.6666666667 + 0.8402777775 = 1.5069444442
0.8402777775 + -1.833333333a + a2 = 1.5069444442

Factor a perfect square on the left side:
(a + -0.9166666665)(a + -0.9166666665) = 1.5069444442

Calculate the square root of the right side: 1.227576655

Break this problem into two subproblems by setting 
(a + -0.9166666665) equal to 1.227576655 and -1.227576655.

Subproblem 1
a + -0.9166666665 = 1.227576655

Simplifying
a + -0.9166666665 = 1.227576655

Reorder the terms:
-0.9166666665 + a = 1.227576655

Solving
-0.9166666665 + a = 1.227576655

Solving for variable 'a'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + a = 1.227576655 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + a = 1.227576655 + 0.9166666665
a = 1.227576655 + 0.9166666665

Combine like terms: 1.227576655 + 0.9166666665 = 2.1442433215
a = 2.1442433215

Simplifying
a = 2.1442433215

Subproblem 2
a + -0.9166666665 = -1.227576655

Simplifying
a + -0.9166666665 = -1.227576655

Reorder the terms:
-0.9166666665 + a = -1.227576655

Solving
-0.9166666665 + a = -1.227576655

Solving for variable 'a'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + a = -1.227576655 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + a = -1.227576655 + 0.9166666665
a = -1.227576655 + 0.9166666665

Combine like terms: -1.227576655 + 0.9166666665 = -0.3109099885
a = -0.3109099885

Simplifying
a = -0.3109099885

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.1442433215, -0.3109099885}
Solution
a = {0, 2.1442433215, -0.3109099885}