8a(3a^2-4a-6)-3a(a-5)=

Solution for 8a(3a^2-4a-6)-3a(a-5)= equation:

Simplifying
8a(3a2 + -4a + -6) + -3a(a + -5) = 0

Reorder the terms:
8a(-6 + -4a + 3a2) + -3a(a + -5) = 0
(-6 * 8a + -4a * 8a + 3a2 * 8a) + -3a(a + -5) = 0
(-48a + -32a2 + 24a3) + -3a(a + -5) = 0

Reorder the terms:
-48a + -32a2 + 24a3 + -3a(-5 + a) = 0
-48a + -32a2 + 24a3 + (-5 * -3a + a * -3a) = 0
-48a + -32a2 + 24a3 + (15a + -3a2) = 0

Reorder the terms:
-48a + 15a + -32a2 + -3a2 + 24a3 = 0

Combine like terms: -48a + 15a = -33a
-33a + -32a2 + -3a2 + 24a3 = 0

Combine like terms: -32a2 + -3a2 = -35a2
-33a + -35a2 + 24a3 = 0

Solving
-33a + -35a2 + 24a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-33 + -35a + 24a2) = 0

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 '(-33 + -35a + 24a2)' equal to zero and attempt to solve:

Simplifying
-33 + -35a + 24a2 = 0

Solving
-33 + -35a + 24a2 = 0

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

Divide each side by '24'.
-1.375 + -1.458333333a + a2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + -1.458333333a + 1.375 + a2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + -1.458333333a + a2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + -1.458333333a + a2 = 0 + 1.375
-1.458333333a + a2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
-1.458333333a + a2 = 1.375

The a term is -1.458333333a.  Take half its coefficient (-0.7291666665).
Square it (0.5316840275) and add it to both sides.

Add '0.5316840275' to each side of the equation.
-1.458333333a + 0.5316840275 + a2 = 1.375 + 0.5316840275

Reorder the terms:
0.5316840275 + -1.458333333a + a2 = 1.375 + 0.5316840275

Combine like terms: 1.375 + 0.5316840275 = 1.9066840275
0.5316840275 + -1.458333333a + a2 = 1.9066840275

Factor a perfect square on the left side:
(a + -0.7291666665)(a + -0.7291666665) = 1.9066840275

Calculate the square root of the right side: 1.380827298

Break this problem into two subproblems by setting 
(a + -0.7291666665) equal to 1.380827298 and -1.380827298.

Subproblem 1
a + -0.7291666665 = 1.380827298

Simplifying
a + -0.7291666665 = 1.380827298

Reorder the terms:
-0.7291666665 + a = 1.380827298

Solving
-0.7291666665 + a = 1.380827298

Solving for variable 'a'.

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

Add '0.7291666665' to each side of the equation.
-0.7291666665 + 0.7291666665 + a = 1.380827298 + 0.7291666665

Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000
0.0000000000 + a = 1.380827298 + 0.7291666665
a = 1.380827298 + 0.7291666665

Combine like terms: 1.380827298 + 0.7291666665 = 2.1099939645
a = 2.1099939645

Simplifying
a = 2.1099939645

Subproblem 2
a + -0.7291666665 = -1.380827298

Simplifying
a + -0.7291666665 = -1.380827298

Reorder the terms:
-0.7291666665 + a = -1.380827298

Solving
-0.7291666665 + a = -1.380827298

Solving for variable 'a'.

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

Add '0.7291666665' to each side of the equation.
-0.7291666665 + 0.7291666665 + a = -1.380827298 + 0.7291666665

Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000
0.0000000000 + a = -1.380827298 + 0.7291666665
a = -1.380827298 + 0.7291666665

Combine like terms: -1.380827298 + 0.7291666665 = -0.6516606315
a = -0.6516606315

Simplifying
a = -0.6516606315

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.1099939645, -0.6516606315}
Solution
a = {0, 2.1099939645, -0.6516606315}