6-6a(a-8)=

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

Simplifying
6 + -6a(a + -8) = 0

Reorder the terms:
6 + -6a(-8 + a) = 0
6 + (-8 * -6a + a * -6a) = 0
6 + (48a + -6a2) = 0

Solving
6 + 48a + -6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 8a + -1a2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + 8a + -1a2)' equal to zero and attempt to solve:

Simplifying
1 + 8a + -1a2 = 0

Solving
1 + 8a + -1a2 = 0

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

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

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -8a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + -8a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8a + a2 = 0 + 1
-8a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-8a + a2 = 1

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 = 1 + 16

Reorder the terms:
16 + -8a + a2 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + -8a + a2 = 17

Factor a perfect square on the left side:
(a + -4)(a + -4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(a + -4) equal to 4.123105626 and -4.123105626.

Subproblem 1
a + -4 = 4.123105626

Simplifying
a + -4 = 4.123105626

Reorder the terms:
-4 + a = 4.123105626

Solving
-4 + a = 4.123105626

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 = 4.123105626 + 4

Combine like terms: -4 + 4 = 0
0 + a = 4.123105626 + 4
a = 4.123105626 + 4

Combine like terms: 4.123105626 + 4 = 8.123105626
a = 8.123105626

Simplifying
a = 8.123105626

Subproblem 2
a + -4 = -4.123105626

Simplifying
a + -4 = -4.123105626

Reorder the terms:
-4 + a = -4.123105626

Solving
-4 + a = -4.123105626

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 = -4.123105626 + 4

Combine like terms: -4 + 4 = 0
0 + a = -4.123105626 + 4
a = -4.123105626 + 4

Combine like terms: -4.123105626 + 4 = -0.123105626
a = -0.123105626

Simplifying
a = -0.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.123105626, -0.123105626}
Solution
a = {8.123105626, -0.123105626}