-8a^2-[a(20a^2+8a)]-[5+(6a-5)]=0

Solution for -8a^2-[a(20a^2+8a)]-[5+(6a-5)]=0 equation:

Simplifying
-8a2 + -1[a(20a2 + 8a)] + -1[5 + (6a + -5)] = 0

Reorder the terms:
-8a2 + -1[a(8a + 20a2)] + -1[5 + (6a + -5)] = 0
-8a2 + -1[(8a * a + 20a2 * a)] + -1[5 + (6a + -5)] = 0
-8a2 + -1[(8a2 + 20a3)] + -1[5 + (6a + -5)] = 0
-8a2 + [8a2 * -1 + 20a3 * -1] + -1[5 + (6a + -5)] = 0
-8a2 + [-8a2 + -20a3] + -1[5 + (6a + -5)] = 0

Reorder the terms:
-8a2 + -8a2 + -20a3 + -1[5 + (-5 + 6a)] = 0

Remove parenthesis around (-5 + 6a)
-8a2 + -8a2 + -20a3 + -1[5 + -5 + 6a] = 0

Combine like terms: 5 + -5 = 0
-8a2 + -8a2 + -20a3 + -1[0 + 6a] = 0
-8a2 + -8a2 + -20a3 + -1[6a] = 0

Remove brackets around [6a]
-8a2 + -8a2 + -20a3 + -1 * 6a = 0

Multiply -1 * 6
-8a2 + -8a2 + -20a3 + -6a = 0

Reorder the terms:
-6a + -8a2 + -8a2 + -20a3 = 0

Combine like terms: -8a2 + -8a2 = -16a2
-6a + -16a2 + -20a3 = 0

Solving
-6a + -16a2 + -20a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-2a'.
-2a(3 + 8a + 10a2) = 0

Ignore the factor -2.
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 '(3 + 8a + 10a2)' equal to zero and attempt to solve:

Simplifying
3 + 8a + 10a2 = 0

Solving
3 + 8a + 10a2 = 0

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

Divide each side by '10'.
0.3 + 0.8a + a2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 0.8a + -0.3 + a2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + 0.8a + a2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 0.8a + a2 = 0.0 + -0.3
0.8a + a2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
0.8a + a2 = -0.3

The a term is 0.8a.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8a + 0.16 + a2 = -0.3 + 0.16

Reorder the terms:
0.16 + 0.8a + a2 = -0.3 + 0.16

Combine like terms: -0.3 + 0.16 = -0.14
0.16 + 0.8a + a2 = -0.14

Factor a perfect square on the left side:
(a + 0.4)(a + 0.4) = -0.14

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}