-8a(2a+6)=4-a

Solution for -8a(2a+6)=4-a equation:

Simplifying
-8a(2a + 6) = 4 + -1a

Reorder the terms:
-8a(6 + 2a) = 4 + -1a
(6 * -8a + 2a * -8a) = 4 + -1a
(-48a + -16a2) = 4 + -1a

Solving
-48a + -16a2 = 4 + -1a

Solving for variable 'a'.

Reorder the terms:
-4 + -48a + a + -16a2 = 4 + -1a + -4 + a

Combine like terms: -48a + a = -47a
-4 + -47a + -16a2 = 4 + -1a + -4 + a

Reorder the terms:
-4 + -47a + -16a2 = 4 + -4 + -1a + a

Combine like terms: 4 + -4 = 0
-4 + -47a + -16a2 = 0 + -1a + a
-4 + -47a + -16a2 = -1a + a

Combine like terms: -1a + a = 0
-4 + -47a + -16a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 47a + 16a2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 47a + 16a2)' equal to zero and attempt to solve:

Simplifying
4 + 47a + 16a2 = 0

Solving
4 + 47a + 16a2 = 0

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

Divide each side by '16'.
0.25 + 2.9375a + a2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2.9375a + -0.25 + a2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2.9375a + a2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2.9375a + a2 = 0 + -0.25
2.9375a + a2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2.9375a + a2 = -0.25

The a term is 2.9375a.  Take half its coefficient (1.46875).
Square it (2.157226563) and add it to both sides.

Add '2.157226563' to each side of the equation.
2.9375a + 2.157226563 + a2 = -0.25 + 2.157226563

Reorder the terms:
2.157226563 + 2.9375a + a2 = -0.25 + 2.157226563

Combine like terms: -0.25 + 2.157226563 = 1.907226563
2.157226563 + 2.9375a + a2 = 1.907226563

Factor a perfect square on the left side:
(a + 1.46875)(a + 1.46875) = 1.907226563

Calculate the square root of the right side: 1.381023737

Break this problem into two subproblems by setting 
(a + 1.46875) equal to 1.381023737 and -1.381023737.

Subproblem 1
a + 1.46875 = 1.381023737

Simplifying
a + 1.46875 = 1.381023737

Reorder the terms:
1.46875 + a = 1.381023737

Solving
1.46875 + a = 1.381023737

Solving for variable 'a'.

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

Add '-1.46875' to each side of the equation.
1.46875 + -1.46875 + a = 1.381023737 + -1.46875

Combine like terms: 1.46875 + -1.46875 = 0.00000
0.00000 + a = 1.381023737 + -1.46875
a = 1.381023737 + -1.46875

Combine like terms: 1.381023737 + -1.46875 = -0.087726263
a = -0.087726263

Simplifying
a = -0.087726263

Subproblem 2
a + 1.46875 = -1.381023737

Simplifying
a + 1.46875 = -1.381023737

Reorder the terms:
1.46875 + a = -1.381023737

Solving
1.46875 + a = -1.381023737

Solving for variable 'a'.

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

Add '-1.46875' to each side of the equation.
1.46875 + -1.46875 + a = -1.381023737 + -1.46875

Combine like terms: 1.46875 + -1.46875 = 0.00000
0.00000 + a = -1.381023737 + -1.46875
a = -1.381023737 + -1.46875

Combine like terms: -1.381023737 + -1.46875 = -2.849773737
a = -2.849773737

Simplifying
a = -2.849773737

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.087726263, -2.849773737}
Solution
a = {-0.087726263, -2.849773737}