14=3c^2-6c-4

Solution for 14=3c^2-6c-4 equation:

Simplifying
14 = 3c2 + -6c + -4

Reorder the terms:
14 = -4 + -6c + 3c2

Solving
14 = -4 + -6c + 3c2

Solving for variable 'c'.

Combine like terms: 14 + 4 = 18
18 + 6c + -3c2 = -4 + -6c + 3c2 + 4 + 6c + -3c2

Reorder the terms:
18 + 6c + -3c2 = -4 + 4 + -6c + 6c + 3c2 + -3c2

Combine like terms: -4 + 4 = 0
18 + 6c + -3c2 = 0 + -6c + 6c + 3c2 + -3c2
18 + 6c + -3c2 = -6c + 6c + 3c2 + -3c2

Combine like terms: -6c + 6c = 0
18 + 6c + -3c2 = 0 + 3c2 + -3c2
18 + 6c + -3c2 = 3c2 + -3c2

Combine like terms: 3c2 + -3c2 = 0
18 + 6c + -3c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 2c + -1c2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + 2c + -1c2)' equal to zero and attempt to solve:

Simplifying
6 + 2c + -1c2 = 0

Solving
6 + 2c + -1c2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -2c + c2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2c + 6 + c2 = 0 + 6

Reorder the terms:
-6 + 6 + -2c + c2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2c + c2 = 0 + 6
-2c + c2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2c + c2 = 6

The c term is -2c.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2c + 1 + c2 = 6 + 1

Reorder the terms:
1 + -2c + c2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2c + c2 = 7

Factor a perfect square on the left side:
(c + -1)(c + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(c + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
c + -1 = 2.645751311

Simplifying
c + -1 = 2.645751311

Reorder the terms:
-1 + c = 2.645751311

Solving
-1 + c = 2.645751311

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + c = 2.645751311 + 1
c = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
c = 3.645751311

Simplifying
c = 3.645751311

Subproblem 2
c + -1 = -2.645751311

Simplifying
c + -1 = -2.645751311

Reorder the terms:
-1 + c = -2.645751311

Solving
-1 + c = -2.645751311

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + c = -2.645751311 + 1
c = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
c = -1.645751311

Simplifying
c = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.645751311, -1.645751311}
Solution
c = {3.645751311, -1.645751311}