6(c+5)c=9

Solution for 6(c+5)c=9 equation:

Simplifying
6(c + 5) * c = 9

Reorder the terms:
6(5 + c) * c = 9

Reorder the terms for easier multiplication:
6c(5 + c) = 9
(5 * 6c + c * 6c) = 9
(30c + 6c2) = 9

Solving
30c + 6c2 = 9

Solving for variable 'c'.

Reorder the terms:
-9 + 30c + 6c2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 30c + 6c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 10c + 2c2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + 10c + 2c2)' equal to zero and attempt to solve:

Simplifying
-3 + 10c + 2c2 = 0

Solving
-3 + 10c + 2c2 = 0

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

Divide each side by '2'.
-1.5 + 5c + c2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 5c + 1.5 + c2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 5c + c2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 5c + c2 = 0 + 1.5
5c + c2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
5c + c2 = 1.5

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 = 1.5 + 6.25

Reorder the terms:
6.25 + 5c + c2 = 1.5 + 6.25

Combine like terms: 1.5 + 6.25 = 7.75
6.25 + 5c + c2 = 7.75

Factor a perfect square on the left side:
(c + 2.5)(c + 2.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(c + 2.5) equal to 2.783882181 and -2.783882181.

Subproblem 1
c + 2.5 = 2.783882181

Simplifying
c + 2.5 = 2.783882181

Reorder the terms:
2.5 + c = 2.783882181

Solving
2.5 + c = 2.783882181

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 = 2.783882181 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = 2.783882181 + -2.5
c = 2.783882181 + -2.5

Combine like terms: 2.783882181 + -2.5 = 0.283882181
c = 0.283882181

Simplifying
c = 0.283882181

Subproblem 2
c + 2.5 = -2.783882181

Simplifying
c + 2.5 = -2.783882181

Reorder the terms:
2.5 + c = -2.783882181

Solving
2.5 + c = -2.783882181

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 = -2.783882181 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = -2.783882181 + -2.5
c = -2.783882181 + -2.5

Combine like terms: -2.783882181 + -2.5 = -5.283882181
c = -5.283882181

Simplifying
c = -5.283882181

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.283882181, -5.283882181}
Solution
c = {0.283882181, -5.283882181}