59-(2c+4)=4c(c+5)+c

Solution for 59-(2c+4)=4c(c+5)+c equation:

Simplifying
59 + -1(2c + 4) = 4c(c + 5) + c

Reorder the terms:
59 + -1(4 + 2c) = 4c(c + 5) + c
59 + (4 * -1 + 2c * -1) = 4c(c + 5) + c
59 + (-4 + -2c) = 4c(c + 5) + c

Combine like terms: 59 + -4 = 55
55 + -2c = 4c(c + 5) + c

Reorder the terms:
55 + -2c = 4c(5 + c) + c
55 + -2c = (5 * 4c + c * 4c) + c
55 + -2c = (20c + 4c2) + c

Reorder the terms:
55 + -2c = 20c + c + 4c2

Combine like terms: 20c + c = 21c
55 + -2c = 21c + 4c2

Solving
55 + -2c = 21c + 4c2

Solving for variable 'c'.

Combine like terms: -2c + -21c = -23c
55 + -23c + -4c2 = 21c + 4c2 + -21c + -4c2

Reorder the terms:
55 + -23c + -4c2 = 21c + -21c + 4c2 + -4c2

Combine like terms: 21c + -21c = 0
55 + -23c + -4c2 = 0 + 4c2 + -4c2
55 + -23c + -4c2 = 4c2 + -4c2

Combine like terms: 4c2 + -4c2 = 0
55 + -23c + -4c2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-13.75 + 5.75c + c2 = 0

Move the constant term to the right:

Add '13.75' to each side of the equation.
-13.75 + 5.75c + 13.75 + c2 = 0 + 13.75

Reorder the terms:
-13.75 + 13.75 + 5.75c + c2 = 0 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + 5.75c + c2 = 0 + 13.75
5.75c + c2 = 0 + 13.75

Combine like terms: 0 + 13.75 = 13.75
5.75c + c2 = 13.75

The c term is 5.75c.  Take half its coefficient (2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
5.75c + 8.265625 + c2 = 13.75 + 8.265625

Reorder the terms:
8.265625 + 5.75c + c2 = 13.75 + 8.265625

Combine like terms: 13.75 + 8.265625 = 22.015625
8.265625 + 5.75c + c2 = 22.015625

Factor a perfect square on the left side:
(c + 2.875)(c + 2.875) = 22.015625

Calculate the square root of the right side: 4.692081095

Break this problem into two subproblems by setting 
(c + 2.875) equal to 4.692081095 and -4.692081095.

Subproblem 1
c + 2.875 = 4.692081095

Simplifying
c + 2.875 = 4.692081095

Reorder the terms:
2.875 + c = 4.692081095

Solving
2.875 + c = 4.692081095

Solving for variable 'c'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + c = 4.692081095 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + c = 4.692081095 + -2.875
c = 4.692081095 + -2.875

Combine like terms: 4.692081095 + -2.875 = 1.817081095
c = 1.817081095

Simplifying
c = 1.817081095

Subproblem 2
c + 2.875 = -4.692081095

Simplifying
c + 2.875 = -4.692081095

Reorder the terms:
2.875 + c = -4.692081095

Solving
2.875 + c = -4.692081095

Solving for variable 'c'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + c = -4.692081095 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + c = -4.692081095 + -2.875
c = -4.692081095 + -2.875

Combine like terms: -4.692081095 + -2.875 = -7.567081095
c = -7.567081095

Simplifying
c = -7.567081095

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.817081095, -7.567081095}