4(c+7)c=2

Solution for 4(c+7)c=2 equation:

Simplifying
4(c + 7) * c = 2

Reorder the terms:
4(7 + c) * c = 2

Reorder the terms for easier multiplication:
4c(7 + c) = 2
(7 * 4c + c * 4c) = 2
(28c + 4c2) = 2

Solving
28c + 4c2 = 2

Solving for variable 'c'.

Reorder the terms:
-2 + 28c + 4c2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 28c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 14c + 2c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 14c + 2c2)' equal to zero and attempt to solve:

Simplifying
-1 + 14c + 2c2 = 0

Solving
-1 + 14c + 2c2 = 0

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

Divide each side by '2'.
-0.5 + 7c + c2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 7c + 0.5 + c2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 7c + c2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 7c + c2 = 0 + 0.5
7c + c2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
7c + c2 = 0.5

The c term is 7c.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7c + 12.25 + c2 = 0.5 + 12.25

Reorder the terms:
12.25 + 7c + c2 = 0.5 + 12.25

Combine like terms: 0.5 + 12.25 = 12.75
12.25 + 7c + c2 = 12.75

Factor a perfect square on the left side:
(c + 3.5)(c + 3.5) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(c + 3.5) equal to 3.570714214 and -3.570714214.

Subproblem 1
c + 3.5 = 3.570714214

Simplifying
c + 3.5 = 3.570714214

Reorder the terms:
3.5 + c = 3.570714214

Solving
3.5 + c = 3.570714214

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = 3.570714214 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = 3.570714214 + -3.5
c = 3.570714214 + -3.5

Combine like terms: 3.570714214 + -3.5 = 0.070714214
c = 0.070714214

Simplifying
c = 0.070714214

Subproblem 2
c + 3.5 = -3.570714214

Simplifying
c + 3.5 = -3.570714214

Reorder the terms:
3.5 + c = -3.570714214

Solving
3.5 + c = -3.570714214

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = -3.570714214 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = -3.570714214 + -3.5
c = -3.570714214 + -3.5

Combine like terms: -3.570714214 + -3.5 = -7.070714214
c = -7.070714214

Simplifying
c = -7.070714214

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.070714214, -7.070714214}
Solution
c = {0.070714214, -7.070714214}