10c(5-c)=6-8c

Solution for 10c(5-c)=6-8c equation:

Simplifying
10c(5 + -1c) = 6 + -8c
(5 * 10c + -1c * 10c) = 6 + -8c
(50c + -10c2) = 6 + -8c

Solving
50c + -10c2 = 6 + -8c

Solving for variable 'c'.

Reorder the terms:
-6 + 50c + 8c + -10c2 = 6 + -8c + -6 + 8c

Combine like terms: 50c + 8c = 58c
-6 + 58c + -10c2 = 6 + -8c + -6 + 8c

Reorder the terms:
-6 + 58c + -10c2 = 6 + -6 + -8c + 8c

Combine like terms: 6 + -6 = 0
-6 + 58c + -10c2 = 0 + -8c + 8c
-6 + 58c + -10c2 = -8c + 8c

Combine like terms: -8c + 8c = 0
-6 + 58c + -10c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 29c + -5c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 29c + -5c2)' equal to zero and attempt to solve:

Simplifying
-3 + 29c + -5c2 = 0

Solving
-3 + 29c + -5c2 = 0

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

Divide each side by '-5'.
0.6 + -5.8c + c2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -5.8c + -0.6 + c2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -5.8c + c2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -5.8c + c2 = 0 + -0.6
-5.8c + c2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-5.8c + c2 = -0.6

The c term is -5.8c.  Take half its coefficient (-2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
-5.8c + 8.41 + c2 = -0.6 + 8.41

Reorder the terms:
8.41 + -5.8c + c2 = -0.6 + 8.41

Combine like terms: -0.6 + 8.41 = 7.81
8.41 + -5.8c + c2 = 7.81

Factor a perfect square on the left side:
(c + -2.9)(c + -2.9) = 7.81

Calculate the square root of the right side: 2.794637722

Break this problem into two subproblems by setting 
(c + -2.9) equal to 2.794637722 and -2.794637722.

Subproblem 1
c + -2.9 = 2.794637722

Simplifying
c + -2.9 = 2.794637722

Reorder the terms:
-2.9 + c = 2.794637722

Solving
-2.9 + c = 2.794637722

Solving for variable 'c'.

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

Add '2.9' to each side of the equation.
-2.9 + 2.9 + c = 2.794637722 + 2.9

Combine like terms: -2.9 + 2.9 = 0.0
0.0 + c = 2.794637722 + 2.9
c = 2.794637722 + 2.9

Combine like terms: 2.794637722 + 2.9 = 5.694637722
c = 5.694637722

Simplifying
c = 5.694637722

Subproblem 2
c + -2.9 = -2.794637722

Simplifying
c + -2.9 = -2.794637722

Reorder the terms:
-2.9 + c = -2.794637722

Solving
-2.9 + c = -2.794637722

Solving for variable 'c'.

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

Add '2.9' to each side of the equation.
-2.9 + 2.9 + c = -2.794637722 + 2.9

Combine like terms: -2.9 + 2.9 = 0.0
0.0 + c = -2.794637722 + 2.9
c = -2.794637722 + 2.9

Combine like terms: -2.794637722 + 2.9 = 0.105362278
c = 0.105362278

Simplifying
c = 0.105362278

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {5.694637722, 0.105362278}
Solution
c = {5.694637722, 0.105362278}