48-(3c+4)=4c(c+7)+c

Solution for 48-(3c+4)=4c(c+7)+c equation:

Simplifying
48 + -1(3c + 4) = 4c(c + 7) + c

Reorder the terms:
48 + -1(4 + 3c) = 4c(c + 7) + c
48 + (4 * -1 + 3c * -1) = 4c(c + 7) + c
48 + (-4 + -3c) = 4c(c + 7) + c

Combine like terms: 48 + -4 = 44
44 + -3c = 4c(c + 7) + c

Reorder the terms:
44 + -3c = 4c(7 + c) + c
44 + -3c = (7 * 4c + c * 4c) + c
44 + -3c = (28c + 4c2) + c

Reorder the terms:
44 + -3c = 28c + c + 4c2

Combine like terms: 28c + c = 29c
44 + -3c = 29c + 4c2

Solving
44 + -3c = 29c + 4c2

Solving for variable 'c'.

Combine like terms: -3c + -29c = -32c
44 + -32c + -4c2 = 29c + 4c2 + -29c + -4c2

Reorder the terms:
44 + -32c + -4c2 = 29c + -29c + 4c2 + -4c2

Combine like terms: 29c + -29c = 0
44 + -32c + -4c2 = 0 + 4c2 + -4c2
44 + -32c + -4c2 = 4c2 + -4c2

Combine like terms: 4c2 + -4c2 = 0
44 + -32c + -4c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(11 + -8c + -1c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(11 + -8c + -1c2)' equal to zero and attempt to solve:

Simplifying
11 + -8c + -1c2 = 0

Solving
11 + -8c + -1c2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-11 + 8c + c2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 8c + 11 + c2 = 0 + 11

Reorder the terms:
-11 + 11 + 8c + c2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 8c + c2 = 0 + 11
8c + c2 = 0 + 11

Combine like terms: 0 + 11 = 11
8c + c2 = 11

The c term is 8c.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8c + 16 + c2 = 11 + 16

Reorder the terms:
16 + 8c + c2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + 8c + c2 = 27

Factor a perfect square on the left side:
(c + 4)(c + 4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(c + 4) equal to 5.196152423 and -5.196152423.

Subproblem 1
c + 4 = 5.196152423

Simplifying
c + 4 = 5.196152423

Reorder the terms:
4 + c = 5.196152423

Solving
4 + c = 5.196152423

Solving for variable 'c'.

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

Add '-4' to each side of the equation.
4 + -4 + c = 5.196152423 + -4

Combine like terms: 4 + -4 = 0
0 + c = 5.196152423 + -4
c = 5.196152423 + -4

Combine like terms: 5.196152423 + -4 = 1.196152423
c = 1.196152423

Simplifying
c = 1.196152423

Subproblem 2
c + 4 = -5.196152423

Simplifying
c + 4 = -5.196152423

Reorder the terms:
4 + c = -5.196152423

Solving
4 + c = -5.196152423

Solving for variable 'c'.

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

Add '-4' to each side of the equation.
4 + -4 + c = -5.196152423 + -4

Combine like terms: 4 + -4 = 0
0 + c = -5.196152423 + -4
c = -5.196152423 + -4

Combine like terms: -5.196152423 + -4 = -9.196152423
c = -9.196152423

Simplifying
c = -9.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.196152423, -9.196152423}
Solution
c = {1.196152423, -9.196152423}