18c^2+38c+6=0

Solution for 18c^2+38c+6=0 equation:

Simplifying
18c2 + 38c + 6 = 0

Reorder the terms:
6 + 38c + 18c2 = 0

Solving
6 + 38c + 18c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 19c + 9c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 19c + 9c2)' equal to zero and attempt to solve:

Simplifying
3 + 19c + 9c2 = 0

Solving
3 + 19c + 9c2 = 0

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

Divide each side by '9'.
0.3333333333 + 2.111111111c + c2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 2.111111111c + -0.3333333333 + c2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 2.111111111c + c2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 2.111111111c + c2 = 0 + -0.3333333333
2.111111111c + c2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
2.111111111c + c2 = -0.3333333333

The c term is 2.111111111c.  Take half its coefficient (1.055555556).
Square it (1.114197532) and add it to both sides.

Add '1.114197532' to each side of the equation.
2.111111111c + 1.114197532 + c2 = -0.3333333333 + 1.114197532

Reorder the terms:
1.114197532 + 2.111111111c + c2 = -0.3333333333 + 1.114197532

Combine like terms: -0.3333333333 + 1.114197532 = 0.7808641987
1.114197532 + 2.111111111c + c2 = 0.7808641987

Factor a perfect square on the left side:
(c + 1.055555556)(c + 1.055555556) = 0.7808641987

Calculate the square root of the right side: 0.883665207

Break this problem into two subproblems by setting 
(c + 1.055555556) equal to 0.883665207 and -0.883665207.

Subproblem 1
c + 1.055555556 = 0.883665207

Simplifying
c + 1.055555556 = 0.883665207

Reorder the terms:
1.055555556 + c = 0.883665207

Solving
1.055555556 + c = 0.883665207

Solving for variable 'c'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + c = 0.883665207 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + c = 0.883665207 + -1.055555556
c = 0.883665207 + -1.055555556

Combine like terms: 0.883665207 + -1.055555556 = -0.171890349
c = -0.171890349

Simplifying
c = -0.171890349

Subproblem 2
c + 1.055555556 = -0.883665207

Simplifying
c + 1.055555556 = -0.883665207

Reorder the terms:
1.055555556 + c = -0.883665207

Solving
1.055555556 + c = -0.883665207

Solving for variable 'c'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + c = -0.883665207 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + c = -0.883665207 + -1.055555556
c = -0.883665207 + -1.055555556

Combine like terms: -0.883665207 + -1.055555556 = -1.939220763
c = -1.939220763

Simplifying
c = -1.939220763

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.171890349, -1.939220763}
Solution
c = {-0.171890349, -1.939220763}