0.5c(c+2.8)-c=0.6c+0.3

Solution for 0.5c(c+2.8)-c=0.6c+0.3 equation:

Simplifying
0.5c(c + 2.8) + -1c = 0.6c + 0.3

Reorder the terms:
0.5c(2.8 + c) + -1c = 0.6c + 0.3
(2.8 * 0.5c + c * 0.5c) + -1c = 0.6c + 0.3
(1.4c + 0.5c2) + -1c = 0.6c + 0.3

Reorder the terms:
1.4c + -1c + 0.5c2 = 0.6c + 0.3

Combine like terms: 1.4c + -1c = 0.4c
0.4c + 0.5c2 = 0.6c + 0.3

Reorder the terms:
0.4c + 0.5c2 = 0.3 + 0.6c

Solving
0.4c + 0.5c2 = 0.3 + 0.6c

Solving for variable 'c'.

Reorder the terms:
-0.3 + 0.4c + -0.6c + 0.5c2 = 0.3 + 0.6c + -0.3 + -0.6c

Combine like terms: 0.4c + -0.6c = -0.2c
-0.3 + -0.2c + 0.5c2 = 0.3 + 0.6c + -0.3 + -0.6c

Reorder the terms:
-0.3 + -0.2c + 0.5c2 = 0.3 + -0.3 + 0.6c + -0.6c

Combine like terms: 0.3 + -0.3 = 0.0
-0.3 + -0.2c + 0.5c2 = 0.0 + 0.6c + -0.6c
-0.3 + -0.2c + 0.5c2 = 0.6c + -0.6c

Combine like terms: 0.6c + -0.6c = 0.0
-0.3 + -0.2c + 0.5c2 = 0.0

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

Divide each side by '0.5'.
-0.6 + -0.4c + c2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.4c + 0.6 + c2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.4c + c2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.4c + c2 = 0 + 0.6
-0.4c + c2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.4c + c2 = 0.6

The c term is -0.4c.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4c + 0.04 + c2 = 0.6 + 0.04

Reorder the terms:
0.04 + -0.4c + c2 = 0.6 + 0.04

Combine like terms: 0.6 + 0.04 = 0.64
0.04 + -0.4c + c2 = 0.64

Factor a perfect square on the left side:
(c + -0.2)(c + -0.2) = 0.64

Calculate the square root of the right side: 0.8

Break this problem into two subproblems by setting 
(c + -0.2) equal to 0.8 and -0.8.

Subproblem 1
c + -0.2 = 0.8

Simplifying
c + -0.2 = 0.8

Reorder the terms:
-0.2 + c = 0.8

Solving
-0.2 + c = 0.8

Solving for variable 'c'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + c = 0.8 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + c = 0.8 + 0.2
c = 0.8 + 0.2

Combine like terms: 0.8 + 0.2 = 1
c = 1

Simplifying
c = 1

Subproblem 2
c + -0.2 = -0.8

Simplifying
c + -0.2 = -0.8

Reorder the terms:
-0.2 + c = -0.8

Solving
-0.2 + c = -0.8

Solving for variable 'c'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + c = -0.8 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + c = -0.8 + 0.2
c = -0.8 + 0.2

Combine like terms: -0.8 + 0.2 = -0.6
c = -0.6

Simplifying
c = -0.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1, -0.6}