-3c(-c-24)=-3c-24

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Solution for -3c(-c-24)=-3c-24 equation: 


Simplifying
-3c(-1c + -24) = -3c + -24

Reorder the terms:
-3c(-24 + -1c) = -3c + -24
(-24 * -3c + -1c * -3c) = -3c + -24
(72c + 3c2) = -3c + -24

Reorder the terms:
72c + 3c2 = -24 + -3c

Solving
72c + 3c2 = -24 + -3c

Solving for variable 'c'.

Reorder the terms:
24 + 72c + 3c + 3c2 = -24 + -3c + 24 + 3c

Combine like terms: 72c + 3c = 75c
24 + 75c + 3c2 = -24 + -3c + 24 + 3c

Reorder the terms:
24 + 75c + 3c2 = -24 + 24 + -3c + 3c

Combine like terms: -24 + 24 = 0
24 + 75c + 3c2 = 0 + -3c + 3c
24 + 75c + 3c2 = -3c + 3c

Combine like terms: -3c + 3c = 0
24 + 75c + 3c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 25c + c2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + 25c + c2)' equal to zero and attempt to solve:

Simplifying
8 + 25c + c2 = 0

Solving
8 + 25c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 25c + -8 + c2 = 0 + -8

Reorder the terms:
8 + -8 + 25c + c2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 25c + c2 = 0 + -8
25c + c2 = 0 + -8

Combine like terms: 0 + -8 = -8
25c + c2 = -8

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 = -8 + 156.25

Reorder the terms:
156.25 + 25c + c2 = -8 + 156.25

Combine like terms: -8 + 156.25 = 148.25
156.25 + 25c + c2 = 148.25

Factor a perfect square on the left side:
(c + 12.5)(c + 12.5) = 148.25

Calculate the square root of the right side: 12.175795662

Break this problem into two subproblems by setting 
(c + 12.5) equal to 12.175795662 and -12.175795662.


Subproblem 1
c + 12.5 = 12.175795662

Simplifying
c + 12.5 = 12.175795662

Reorder the terms:
12.5 + c = 12.175795662

Solving
12.5 + c = 12.175795662

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 = 12.175795662 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + c = 12.175795662 + -12.5
c = 12.175795662 + -12.5

Combine like terms: 12.175795662 + -12.5 = -0.324204338
c = -0.324204338

Simplifying
c = -0.324204338


Subproblem 2
c + 12.5 = -12.175795662

Simplifying
c + 12.5 = -12.175795662

Reorder the terms:
12.5 + c = -12.175795662

Solving
12.5 + c = -12.175795662

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 = -12.175795662 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + c = -12.175795662 + -12.5
c = -12.175795662 + -12.5

Combine like terms: -12.175795662 + -12.5 = -24.675795662
c = -24.675795662

Simplifying
c = -24.675795662


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.324204338, -24.675795662}
Solution
c = {-0.324204338, -24.675795662}

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