-3a(a-4)-6=-9

Solution for -3a(a-4)-6=-9 equation:

Simplifying
-3a(a + -4) + -6 = -9

Reorder the terms:
-3a(-4 + a) + -6 = -9
(-4 * -3a + a * -3a) + -6 = -9
(12a + -3a2) + -6 = -9

Reorder the terms:
-6 + 12a + -3a2 = -9

Solving
-6 + 12a + -3a2 = -9

Solving for variable 'a'.

Reorder the terms:
-6 + 9 + 12a + -3a2 = -9 + 9

Combine like terms: -6 + 9 = 3
3 + 12a + -3a2 = -9 + 9

Combine like terms: -9 + 9 = 0
3 + 12a + -3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4a + -1a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 4a + -1a2)' equal to zero and attempt to solve:

Simplifying
1 + 4a + -1a2 = 0

Solving
1 + 4a + -1a2 = 0

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

Divide each side by '-1'.
-1 + -4a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + -4a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4a + a2 = 0 + 1
-4a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4a + a2 = 1

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 1 + 4

Reorder the terms:
4 + -4a + a2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4a + a2 = 5

Factor a perfect square on the left side:
(a + -2)(a + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(a + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1
a + -2 = 2.236067978

Simplifying
a + -2 = 2.236067978

Reorder the terms:
-2 + a = 2.236067978

Solving
-2 + a = 2.236067978

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + a = 2.236067978 + 2
a = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
a = 4.236067978

Simplifying
a = 4.236067978

Subproblem 2
a + -2 = -2.236067978

Simplifying
a + -2 = -2.236067978

Reorder the terms:
-2 + a = -2.236067978

Solving
-2 + a = -2.236067978

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + a = -2.236067978 + 2
a = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
a = -0.236067978

Simplifying
a = -0.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.236067978, -0.236067978}
Solution
a = {4.236067978, -0.236067978}