-4c(-c-8)=-4c-8

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Solution for -4c(-c-8)=-4c-8 equation: 


Simplifying
-4c(-1c + -8) = -4c + -8

Reorder the terms:
-4c(-8 + -1c) = -4c + -8
(-8 * -4c + -1c * -4c) = -4c + -8
(32c + 4c2) = -4c + -8

Reorder the terms:
32c + 4c2 = -8 + -4c

Solving
32c + 4c2 = -8 + -4c

Solving for variable 'c'.

Reorder the terms:
8 + 32c + 4c + 4c2 = -8 + -4c + 8 + 4c

Combine like terms: 32c + 4c = 36c
8 + 36c + 4c2 = -8 + -4c + 8 + 4c

Reorder the terms:
8 + 36c + 4c2 = -8 + 8 + -4c + 4c

Combine like terms: -8 + 8 = 0
8 + 36c + 4c2 = 0 + -4c + 4c
8 + 36c + 4c2 = -4c + 4c

Combine like terms: -4c + 4c = 0
8 + 36c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 9c + c2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + 9c + c2)' equal to zero and attempt to solve:

Simplifying
2 + 9c + c2 = 0

Solving
2 + 9c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 9c + -2 + c2 = 0 + -2

Reorder the terms:
2 + -2 + 9c + c2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9c + c2 = 0 + -2
9c + c2 = 0 + -2

Combine like terms: 0 + -2 = -2
9c + c2 = -2

The c term is 9c.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9c + 20.25 + c2 = -2 + 20.25

Reorder the terms:
20.25 + 9c + c2 = -2 + 20.25

Combine like terms: -2 + 20.25 = 18.25
20.25 + 9c + c2 = 18.25

Factor a perfect square on the left side:
(c + 4.5)(c + 4.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(c + 4.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
c + 4.5 = 4.272001873

Simplifying
c + 4.5 = 4.272001873

Reorder the terms:
4.5 + c = 4.272001873

Solving
4.5 + c = 4.272001873

Solving for variable 'c'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + c = 4.272001873 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = 4.272001873 + -4.5
c = 4.272001873 + -4.5

Combine like terms: 4.272001873 + -4.5 = -0.227998127
c = -0.227998127

Simplifying
c = -0.227998127


Subproblem 2
c + 4.5 = -4.272001873

Simplifying
c + 4.5 = -4.272001873

Reorder the terms:
4.5 + c = -4.272001873

Solving
4.5 + c = -4.272001873

Solving for variable 'c'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + c = -4.272001873 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = -4.272001873 + -4.5
c = -4.272001873 + -4.5

Combine like terms: -4.272001873 + -4.5 = -8.772001873
c = -8.772001873

Simplifying
c = -8.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.227998127, -8.772001873}
Solution
c = {-0.227998127, -8.772001873}

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