2c^2+9c+6+9c=14

Solution for 2c^2+9c+6+9c=14 equation:

Simplifying
2c2 + 9c + 6 + 9c = 14

Reorder the terms:
6 + 9c + 9c + 2c2 = 14

Combine like terms: 9c + 9c = 18c
6 + 18c + 2c2 = 14

Solving
6 + 18c + 2c2 = 14

Solving for variable 'c'.

Reorder the terms:
6 + -14 + 18c + 2c2 = 14 + -14

Combine like terms: 6 + -14 = -8
-8 + 18c + 2c2 = 14 + -14

Combine like terms: 14 + -14 = 0
-8 + 18c + 2c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 9c + c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 9c + c2)' equal to zero and attempt to solve:

Simplifying
-4 + 9c + c2 = 0

Solving
-4 + 9c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 9c + 4 + c2 = 0 + 4

Reorder the terms:
-4 + 4 + 9c + c2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 9c + c2 = 0 + 4
9c + c2 = 0 + 4

Combine like terms: 0 + 4 = 4
9c + c2 = 4

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 = 4 + 20.25

Reorder the terms:
20.25 + 9c + c2 = 4 + 20.25

Combine like terms: 4 + 20.25 = 24.25
20.25 + 9c + c2 = 24.25

Factor a perfect square on the left side:
(c + 4.5)(c + 4.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(c + 4.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
c + 4.5 = 4.924428901

Simplifying
c + 4.5 = 4.924428901

Reorder the terms:
4.5 + c = 4.924428901

Solving
4.5 + c = 4.924428901

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 = 4.924428901 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = 4.924428901 + -4.5
c = 4.924428901 + -4.5

Combine like terms: 4.924428901 + -4.5 = 0.424428901
c = 0.424428901

Simplifying
c = 0.424428901

Subproblem 2
c + 4.5 = -4.924428901

Simplifying
c + 4.5 = -4.924428901

Reorder the terms:
4.5 + c = -4.924428901

Solving
4.5 + c = -4.924428901

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 = -4.924428901 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = -4.924428901 + -4.5
c = -4.924428901 + -4.5

Combine like terms: -4.924428901 + -4.5 = -9.424428901
c = -9.424428901

Simplifying
c = -9.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.424428901, -9.424428901}
Solution
c = {0.424428901, -9.424428901}