10(c+7)c=2

Solution for 10(c+7)c=2 equation:

Simplifying
10(c + 7) * c = 2

Reorder the terms:
10(7 + c) * c = 2

Reorder the terms for easier multiplication:
10c(7 + c) = 2
(7 * 10c + c * 10c) = 2
(70c + 10c2) = 2

Solving
70c + 10c2 = 2

Solving for variable 'c'.

Reorder the terms:
-2 + 70c + 10c2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 70c + 10c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 35c + 5c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 35c + 5c2)' equal to zero and attempt to solve:

Simplifying
-1 + 35c + 5c2 = 0

Solving
-1 + 35c + 5c2 = 0

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

Divide each side by '5'.
-0.2 + 7c + c2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 7c + 0.2 + c2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 7c + c2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 7c + c2 = 0 + 0.2
7c + c2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
7c + c2 = 0.2

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 = 0.2 + 12.25

Reorder the terms:
12.25 + 7c + c2 = 0.2 + 12.25

Combine like terms: 0.2 + 12.25 = 12.45
12.25 + 7c + c2 = 12.45

Factor a perfect square on the left side:
(c + 3.5)(c + 3.5) = 12.45

Calculate the square root of the right side: 3.528455753

Break this problem into two subproblems by setting 
(c + 3.5) equal to 3.528455753 and -3.528455753.

Subproblem 1
c + 3.5 = 3.528455753

Simplifying
c + 3.5 = 3.528455753

Reorder the terms:
3.5 + c = 3.528455753

Solving
3.5 + c = 3.528455753

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 = 3.528455753 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = 3.528455753 + -3.5
c = 3.528455753 + -3.5

Combine like terms: 3.528455753 + -3.5 = 0.028455753
c = 0.028455753

Simplifying
c = 0.028455753

Subproblem 2
c + 3.5 = -3.528455753

Simplifying
c + 3.5 = -3.528455753

Reorder the terms:
3.5 + c = -3.528455753

Solving
3.5 + c = -3.528455753

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 = -3.528455753 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = -3.528455753 + -3.5
c = -3.528455753 + -3.5

Combine like terms: -3.528455753 + -3.5 = -7.028455753
c = -7.028455753

Simplifying
c = -7.028455753

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.028455753, -7.028455753}
Solution
c = {0.028455753, -7.028455753}