-4c(-c-24)=-4c-24

Solution for -4c(-c-24)=-4c-24 equation:

Simplifying
-4c(-1c + -24) = -4c + -24

Reorder the terms:
-4c(-24 + -1c) = -4c + -24
(-24 * -4c + -1c * -4c) = -4c + -24
(96c + 4c2) = -4c + -24

Reorder the terms:
96c + 4c2 = -24 + -4c

Solving
96c + 4c2 = -24 + -4c

Solving for variable 'c'.

Reorder the terms:
24 + 96c + 4c + 4c2 = -24 + -4c + 24 + 4c

Combine like terms: 96c + 4c = 100c
24 + 100c + 4c2 = -24 + -4c + 24 + 4c

Reorder the terms:
24 + 100c + 4c2 = -24 + 24 + -4c + 4c

Combine like terms: -24 + 24 = 0
24 + 100c + 4c2 = 0 + -4c + 4c
24 + 100c + 4c2 = -4c + 4c

Combine like terms: -4c + 4c = 0
24 + 100c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 25c + c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + 25c + c2)' equal to zero and attempt to solve:

Simplifying
6 + 25c + c2 = 0

Solving
6 + 25c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 25c + -6 + c2 = 0 + -6

Reorder the terms:
6 + -6 + 25c + c2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 25c + c2 = 0 + -6
25c + c2 = 0 + -6

Combine like terms: 0 + -6 = -6
25c + c2 = -6

The c term is 25c.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25c + 156.25 + c2 = -6 + 156.25

Reorder the terms:
156.25 + 25c + c2 = -6 + 156.25

Combine like terms: -6 + 156.25 = 150.25
156.25 + 25c + c2 = 150.25

Factor a perfect square on the left side:
(c + 12.5)(c + 12.5) = 150.25

Calculate the square root of the right side: 12.257650672

Break this problem into two subproblems by setting 
(c + 12.5) equal to 12.257650672 and -12.257650672.

Subproblem 1
c + 12.5 = 12.257650672

Simplifying
c + 12.5 = 12.257650672

Reorder the terms:
12.5 + c = 12.257650672

Solving
12.5 + c = 12.257650672

Solving for variable 'c'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + c = 12.257650672 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + c = 12.257650672 + -12.5
c = 12.257650672 + -12.5

Combine like terms: 12.257650672 + -12.5 = -0.242349328
c = -0.242349328

Simplifying
c = -0.242349328

Subproblem 2
c + 12.5 = -12.257650672

Simplifying
c + 12.5 = -12.257650672

Reorder the terms:
12.5 + c = -12.257650672

Solving
12.5 + c = -12.257650672

Solving for variable 'c'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + c = -12.257650672 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + c = -12.257650672 + -12.5
c = -12.257650672 + -12.5

Combine like terms: -12.257650672 + -12.5 = -24.757650672
c = -24.757650672

Simplifying
c = -24.757650672

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.242349328, -24.757650672}
Solution
c = {-0.242349328, -24.757650672}