38-(2c+4)=4(c+5)c

Solution for 38-(2c+4)=4(c+5)c equation:

Simplifying
38 + -1(2c + 4) = 4(c + 5) * c

Reorder the terms:
38 + -1(4 + 2c) = 4(c + 5) * c
38 + (4 * -1 + 2c * -1) = 4(c + 5) * c
38 + (-4 + -2c) = 4(c + 5) * c

Combine like terms: 38 + -4 = 34
34 + -2c = 4(c + 5) * c

Reorder the terms:
34 + -2c = 4(5 + c) * c

Reorder the terms for easier multiplication:
34 + -2c = 4c(5 + c)
34 + -2c = (5 * 4c + c * 4c)
34 + -2c = (20c + 4c2)

Solving
34 + -2c = 20c + 4c2

Solving for variable 'c'.

Combine like terms: -2c + -20c = -22c
34 + -22c + -4c2 = 20c + 4c2 + -20c + -4c2

Reorder the terms:
34 + -22c + -4c2 = 20c + -20c + 4c2 + -4c2

Combine like terms: 20c + -20c = 0
34 + -22c + -4c2 = 0 + 4c2 + -4c2
34 + -22c + -4c2 = 4c2 + -4c2

Combine like terms: 4c2 + -4c2 = 0
34 + -22c + -4c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -11c + -2c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(17 + -11c + -2c2)' equal to zero and attempt to solve:

Simplifying
17 + -11c + -2c2 = 0

Solving
17 + -11c + -2c2 = 0

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

Divide each side by '-2'.
-8.5 + 5.5c + c2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 5.5c + 8.5 + c2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 5.5c + c2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 5.5c + c2 = 0 + 8.5
5.5c + c2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
5.5c + c2 = 8.5

The c term is 5.5c.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5c + 7.5625 + c2 = 8.5 + 7.5625

Reorder the terms:
7.5625 + 5.5c + c2 = 8.5 + 7.5625

Combine like terms: 8.5 + 7.5625 = 16.0625
7.5625 + 5.5c + c2 = 16.0625

Factor a perfect square on the left side:
(c + 2.75)(c + 2.75) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(c + 2.75) equal to 4.007804885 and -4.007804885.

Subproblem 1
c + 2.75 = 4.007804885

Simplifying
c + 2.75 = 4.007804885

Reorder the terms:
2.75 + c = 4.007804885

Solving
2.75 + c = 4.007804885

Solving for variable 'c'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + c = 4.007804885 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + c = 4.007804885 + -2.75
c = 4.007804885 + -2.75

Combine like terms: 4.007804885 + -2.75 = 1.257804885
c = 1.257804885

Simplifying
c = 1.257804885

Subproblem 2
c + 2.75 = -4.007804885

Simplifying
c + 2.75 = -4.007804885

Reorder the terms:
2.75 + c = -4.007804885

Solving
2.75 + c = -4.007804885

Solving for variable 'c'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + c = -4.007804885 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + c = -4.007804885 + -2.75
c = -4.007804885 + -2.75

Combine like terms: -4.007804885 + -2.75 = -6.757804885
c = -6.757804885

Simplifying
c = -6.757804885

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.257804885, -6.757804885}
Solution
c = {1.257804885, -6.757804885}