6(c+5)c=4

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Solution for 6(c+5)c=4 equation: 


Simplifying
6(c + 5) * c = 4

Reorder the terms:
6(5 + c) * c = 4

Reorder the terms for easier multiplication:
6c(5 + c) = 4
(5 * 6c + c * 6c) = 4
(30c + 6c2) = 4

Solving
30c + 6c2 = 4

Solving for variable 'c'.

Reorder the terms:
-4 + 30c + 6c2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 30c + 6c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 15c + 3c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 15c + 3c2)' equal to zero and attempt to solve:

Simplifying
-2 + 15c + 3c2 = 0

Solving
-2 + 15c + 3c2 = 0

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

Divide each side by '3'.
-0.6666666667 + 5c + c2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 5c + 0.6666666667 + c2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 5c + c2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 5c + c2 = 0 + 0.6666666667
5c + c2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
5c + c2 = 0.6666666667

The c term is 5c.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5c + 6.25 + c2 = 0.6666666667 + 6.25

Reorder the terms:
6.25 + 5c + c2 = 0.6666666667 + 6.25

Combine like terms: 0.6666666667 + 6.25 = 6.9166666667
6.25 + 5c + c2 = 6.9166666667

Factor a perfect square on the left side:
(c + 2.5)(c + 2.5) = 6.9166666667

Calculate the square root of the right side: 2.62995564

Break this problem into two subproblems by setting 
(c + 2.5) equal to 2.62995564 and -2.62995564.


Subproblem 1
c + 2.5 = 2.62995564

Simplifying
c + 2.5 = 2.62995564

Reorder the terms:
2.5 + c = 2.62995564

Solving
2.5 + c = 2.62995564

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = 2.62995564 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = 2.62995564 + -2.5
c = 2.62995564 + -2.5

Combine like terms: 2.62995564 + -2.5 = 0.12995564
c = 0.12995564

Simplifying
c = 0.12995564


Subproblem 2
c + 2.5 = -2.62995564

Simplifying
c + 2.5 = -2.62995564

Reorder the terms:
2.5 + c = -2.62995564

Solving
2.5 + c = -2.62995564

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = -2.62995564 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = -2.62995564 + -2.5
c = -2.62995564 + -2.5

Combine like terms: -2.62995564 + -2.5 = -5.12995564
c = -5.12995564

Simplifying
c = -5.12995564


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.12995564, -5.12995564}
Solution
c = {0.12995564, -5.12995564}

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