4c(2c+2)=20

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Solution for 4c(2c+2)=20 equation: 


Simplifying
4c(2c + 2) = 20

Reorder the terms:
4c(2 + 2c) = 20
(2 * 4c + 2c * 4c) = 20
(8c + 8c2) = 20

Solving
8c + 8c2 = 20

Solving for variable 'c'.

Reorder the terms:
-20 + 8c + 8c2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 8c + 8c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 2c + 2c2) = 0

Ignore the factor 4.

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

Simplifying
-5 + 2c + 2c2 = 0

Solving
-5 + 2c + 2c2 = 0

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

Divide each side by '2'.
-2.5 + c + c2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + c + 2.5 + c2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + c + c2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + c + c2 = 0 + 2.5
c + c2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
c + c2 = 2.5

The c term is c.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + c2 = 2.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + c2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
1.25 + c2 = 2.75

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(c + 0.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
c + 0.5 = 1.658312395

Simplifying
c + 0.5 = 1.658312395

Reorder the terms:
0.5 + c = 1.658312395

Solving
0.5 + c = 1.658312395

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = 1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 1.658312395 + -0.5
c = 1.658312395 + -0.5

Combine like terms: 1.658312395 + -0.5 = 1.158312395
c = 1.158312395

Simplifying
c = 1.158312395


Subproblem 2
c + 0.5 = -1.658312395

Simplifying
c + 0.5 = -1.658312395

Reorder the terms:
0.5 + c = -1.658312395

Solving
0.5 + c = -1.658312395

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = -1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -1.658312395 + -0.5
c = -1.658312395 + -0.5

Combine like terms: -1.658312395 + -0.5 = -2.158312395
c = -2.158312395

Simplifying
c = -2.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.158312395, -2.158312395}
Solution
c = {1.158312395, -2.158312395}

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