0.2c(10-5c)=5c-16

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Solution for 0.2c(10-5c)=5c-16 equation: 


Simplifying
0.2c(10 + -5c) = 5c + -16
(10 * 0.2c + -5c * 0.2c) = 5c + -16
(2c + -1c2) = 5c + -16

Reorder the terms:
2c + -1c2 = -16 + 5c

Solving
2c + -1c2 = -16 + 5c

Solving for variable 'c'.

Reorder the terms:
16 + 2c + -5c + -1c2 = -16 + 5c + 16 + -5c

Combine like terms: 2c + -5c = -3c
16 + -3c + -1c2 = -16 + 5c + 16 + -5c

Reorder the terms:
16 + -3c + -1c2 = -16 + 16 + 5c + -5c

Combine like terms: -16 + 16 = 0
16 + -3c + -1c2 = 0 + 5c + -5c
16 + -3c + -1c2 = 5c + -5c

Combine like terms: 5c + -5c = 0
16 + -3c + -1c2 = 0

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

Divide each side by '-1'.
-16 + 3c + c2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3c + 16 + c2 = 0 + 16

Reorder the terms:
-16 + 16 + 3c + c2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3c + c2 = 0 + 16
3c + c2 = 0 + 16

Combine like terms: 0 + 16 = 16
3c + c2 = 16

The c term is 3c.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3c + 2.25 + c2 = 16 + 2.25

Reorder the terms:
2.25 + 3c + c2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3c + c2 = 18.25

Factor a perfect square on the left side:
(c + 1.5)(c + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(c + 1.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
c + 1.5 = 4.272001873

Simplifying
c + 1.5 = 4.272001873

Reorder the terms:
1.5 + c = 4.272001873

Solving
1.5 + c = 4.272001873

Solving for variable 'c'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + c = 4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + c = 4.272001873 + -1.5
c = 4.272001873 + -1.5

Combine like terms: 4.272001873 + -1.5 = 2.772001873
c = 2.772001873

Simplifying
c = 2.772001873


Subproblem 2
c + 1.5 = -4.272001873

Simplifying
c + 1.5 = -4.272001873

Reorder the terms:
1.5 + c = -4.272001873

Solving
1.5 + c = -4.272001873

Solving for variable 'c'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + c = -4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + c = -4.272001873 + -1.5
c = -4.272001873 + -1.5

Combine like terms: -4.272001873 + -1.5 = -5.772001873
c = -5.772001873

Simplifying
c = -5.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.772001873, -5.772001873}

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