3(c+9)c=5

Solution for 3(c+9)c=5 equation:

Simplifying
3(c + 9) * c = 5

Reorder the terms:
3(9 + c) * c = 5

Reorder the terms for easier multiplication:
3c(9 + c) = 5
(9 * 3c + c * 3c) = 5
(27c + 3c2) = 5

Solving
27c + 3c2 = 5

Solving for variable 'c'.

Reorder the terms:
-5 + 27c + 3c2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 27c + 3c2 = 0

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

Divide each side by '3'.
-1.666666667 + 9c + c2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 9c + 1.666666667 + c2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 9c + c2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 9c + c2 = 0 + 1.666666667
9c + c2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
9c + c2 = 1.666666667

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 = 1.666666667 + 20.25

Reorder the terms:
20.25 + 9c + c2 = 1.666666667 + 20.25

Combine like terms: 1.666666667 + 20.25 = 21.916666667
20.25 + 9c + c2 = 21.916666667

Factor a perfect square on the left side:
(c + 4.5)(c + 4.5) = 21.916666667

Calculate the square root of the right side: 4.681523968

Break this problem into two subproblems by setting 
(c + 4.5) equal to 4.681523968 and -4.681523968.

Subproblem 1
c + 4.5 = 4.681523968

Simplifying
c + 4.5 = 4.681523968

Reorder the terms:
4.5 + c = 4.681523968

Solving
4.5 + c = 4.681523968

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 = 4.681523968 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = 4.681523968 + -4.5
c = 4.681523968 + -4.5

Combine like terms: 4.681523968 + -4.5 = 0.181523968
c = 0.181523968

Simplifying
c = 0.181523968

Subproblem 2
c + 4.5 = -4.681523968

Simplifying
c + 4.5 = -4.681523968

Reorder the terms:
4.5 + c = -4.681523968

Solving
4.5 + c = -4.681523968

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 = -4.681523968 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = -4.681523968 + -4.5
c = -4.681523968 + -4.5

Combine like terms: -4.681523968 + -4.5 = -9.181523968
c = -9.181523968

Simplifying
c = -9.181523968

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.181523968, -9.181523968}