-2(a-8)6a=36

Solution for -2(a-8)6a=36 equation:

Simplifying
-2(a + -8) * 6a = 36

Reorder the terms:
-2(-8 + a) * 6a = 36

Reorder the terms for easier multiplication:
-2 * 6a(-8 + a) = 36

Multiply -2 * 6
-12a(-8 + a) = 36
(-8 * -12a + a * -12a) = 36
(96a + -12a2) = 36

Solving
96a + -12a2 = 36

Solving for variable 'a'.

Reorder the terms:
-36 + 96a + -12a2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 96a + -12a2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + 8a + -1a2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-3 + 8a + -1a2)' equal to zero and attempt to solve:

Simplifying
-3 + 8a + -1a2 = 0

Solving
-3 + 8a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -8a + a2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + -8a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8a + a2 = 0 + -3
-8a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8a + a2 = -3

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = -3 + 16

Reorder the terms:
16 + -8a + a2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + -8a + a2 = 13

Factor a perfect square on the left side:
(a + -4)(a + -4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(a + -4) equal to 3.605551275 and -3.605551275.

Subproblem 1
a + -4 = 3.605551275

Simplifying
a + -4 = 3.605551275

Reorder the terms:
-4 + a = 3.605551275

Solving
-4 + a = 3.605551275

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + a = 3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + a = 3.605551275 + 4
a = 3.605551275 + 4

Combine like terms: 3.605551275 + 4 = 7.605551275
a = 7.605551275

Simplifying
a = 7.605551275

Subproblem 2
a + -4 = -3.605551275

Simplifying
a + -4 = -3.605551275

Reorder the terms:
-4 + a = -3.605551275

Solving
-4 + a = -3.605551275

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + a = -3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + a = -3.605551275 + 4
a = -3.605551275 + 4

Combine like terms: -3.605551275 + 4 = 0.394448725
a = 0.394448725

Simplifying
a = 0.394448725

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.605551275, 0.394448725}
Solution
a = {7.605551275, 0.394448725}