4(c+5)11c=110

Solution for 4(c+5)11c=110 equation:

Simplifying
4(c + 5) * 11c = 110

Reorder the terms:
4(5 + c) * 11c = 110

Reorder the terms for easier multiplication:
4 * 11c(5 + c) = 110

Multiply 4 * 11
44c(5 + c) = 110
(5 * 44c + c * 44c) = 110
(220c + 44c2) = 110

Solving
220c + 44c2 = 110

Solving for variable 'c'.

Reorder the terms:
-110 + 220c + 44c2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + 220c + 44c2 = 0

Factor out the Greatest Common Factor (GCF), '22'.
22(-5 + 10c + 2c2) = 0

Ignore the factor 22.
Subproblem 1
Set the factor '(-5 + 10c + 2c2)' equal to zero and attempt to solve:

Simplifying
-5 + 10c + 2c2 = 0

Solving
-5 + 10c + 2c2 = 0

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

Divide each side by '2'.
-2.5 + 5c + c2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 5c + 2.5 + c2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 5c + c2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 5c + c2 = 0 + 2.5
5c + c2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
5c + c2 = 2.5

The c term is 5c.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5c + 6.25 + c2 = 2.5 + 6.25

Reorder the terms:
6.25 + 5c + c2 = 2.5 + 6.25

Combine like terms: 2.5 + 6.25 = 8.75
6.25 + 5c + c2 = 8.75

Factor a perfect square on the left side:
(c + 2.5)(c + 2.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(c + 2.5) equal to 2.958039892 and -2.958039892.

Subproblem 1
c + 2.5 = 2.958039892

Simplifying
c + 2.5 = 2.958039892

Reorder the terms:
2.5 + c = 2.958039892

Solving
2.5 + c = 2.958039892

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = 2.958039892 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = 2.958039892 + -2.5
c = 2.958039892 + -2.5

Combine like terms: 2.958039892 + -2.5 = 0.458039892
c = 0.458039892

Simplifying
c = 0.458039892

Subproblem 2
c + 2.5 = -2.958039892

Simplifying
c + 2.5 = -2.958039892

Reorder the terms:
2.5 + c = -2.958039892

Solving
2.5 + c = -2.958039892

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = -2.958039892 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = -2.958039892 + -2.5
c = -2.958039892 + -2.5

Combine like terms: -2.958039892 + -2.5 = -5.458039892
c = -5.458039892

Simplifying
c = -5.458039892

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.458039892, -5.458039892}
Solution
c = {0.458039892, -5.458039892}