4(3+c)c=c+4

Solution for 4(3+c)c=c+4 equation:

Simplifying
4(3 + c) * c = c + 4

Reorder the terms for easier multiplication:
4c(3 + c) = c + 4
(3 * 4c + c * 4c) = c + 4
(12c + 4c2) = c + 4

Reorder the terms:
12c + 4c2 = 4 + c

Solving
12c + 4c2 = 4 + c

Solving for variable 'c'.

Reorder the terms:
-4 + 12c + -1c + 4c2 = 4 + c + -4 + -1c

Combine like terms: 12c + -1c = 11c
-4 + 11c + 4c2 = 4 + c + -4 + -1c

Reorder the terms:
-4 + 11c + 4c2 = 4 + -4 + c + -1c

Combine like terms: 4 + -4 = 0
-4 + 11c + 4c2 = 0 + c + -1c
-4 + 11c + 4c2 = c + -1c

Combine like terms: c + -1c = 0
-4 + 11c + 4c2 = 0

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

Divide each side by '4'.
-1 + 2.75c + c2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.75c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.75c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.75c + c2 = 0 + 1
2.75c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.75c + c2 = 1

The c term is 2.75c.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75c + 1.890625 + c2 = 1 + 1.890625

Reorder the terms:
1.890625 + 2.75c + c2 = 1 + 1.890625

Combine like terms: 1 + 1.890625 = 2.890625
1.890625 + 2.75c + c2 = 2.890625

Factor a perfect square on the left side:
(c + 1.375)(c + 1.375) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(c + 1.375) equal to 1.700183814 and -1.700183814.

Subproblem 1
c + 1.375 = 1.700183814

Simplifying
c + 1.375 = 1.700183814

Reorder the terms:
1.375 + c = 1.700183814

Solving
1.375 + c = 1.700183814

Solving for variable 'c'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + c = 1.700183814 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + c = 1.700183814 + -1.375
c = 1.700183814 + -1.375

Combine like terms: 1.700183814 + -1.375 = 0.325183814
c = 0.325183814

Simplifying
c = 0.325183814

Subproblem 2
c + 1.375 = -1.700183814

Simplifying
c + 1.375 = -1.700183814

Reorder the terms:
1.375 + c = -1.700183814

Solving
1.375 + c = -1.700183814

Solving for variable 'c'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + c = -1.700183814 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + c = -1.700183814 + -1.375
c = -1.700183814 + -1.375

Combine like terms: -1.700183814 + -1.375 = -3.075183814
c = -3.075183814

Simplifying
c = -3.075183814

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.325183814, -3.075183814}