4c(6c+3)=92

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Solution for 4c(6c+3)=92 equation: 


Simplifying
4c(6c + 3) = 92

Reorder the terms:
4c(3 + 6c) = 92
(3 * 4c + 6c * 4c) = 92
(12c + 24c2) = 92

Solving
12c + 24c2 = 92

Solving for variable 'c'.

Reorder the terms:
-92 + 12c + 24c2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + 12c + 24c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + 3c + 6c2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-23 + 3c + 6c2)' equal to zero and attempt to solve:

Simplifying
-23 + 3c + 6c2 = 0

Solving
-23 + 3c + 6c2 = 0

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

Divide each side by '6'.
-3.833333333 + 0.5c + c2 = 0

Move the constant term to the right:

Add '3.833333333' to each side of the equation.
-3.833333333 + 0.5c + 3.833333333 + c2 = 0 + 3.833333333

Reorder the terms:
-3.833333333 + 3.833333333 + 0.5c + c2 = 0 + 3.833333333

Combine like terms: -3.833333333 + 3.833333333 = 0.000000000
0.000000000 + 0.5c + c2 = 0 + 3.833333333
0.5c + c2 = 0 + 3.833333333

Combine like terms: 0 + 3.833333333 = 3.833333333
0.5c + c2 = 3.833333333

The c term is 0.5c.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5c + 0.0625 + c2 = 3.833333333 + 0.0625

Reorder the terms:
0.0625 + 0.5c + c2 = 3.833333333 + 0.0625

Combine like terms: 3.833333333 + 0.0625 = 3.895833333
0.0625 + 0.5c + c2 = 3.895833333

Factor a perfect square on the left side:
(c + 0.25)(c + 0.25) = 3.895833333

Calculate the square root of the right side: 1.973786547

Break this problem into two subproblems by setting 
(c + 0.25) equal to 1.973786547 and -1.973786547.


Subproblem 1
c + 0.25 = 1.973786547

Simplifying
c + 0.25 = 1.973786547

Reorder the terms:
0.25 + c = 1.973786547

Solving
0.25 + c = 1.973786547

Solving for variable 'c'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + c = 1.973786547 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + c = 1.973786547 + -0.25
c = 1.973786547 + -0.25

Combine like terms: 1.973786547 + -0.25 = 1.723786547
c = 1.723786547

Simplifying
c = 1.723786547


Subproblem 2
c + 0.25 = -1.973786547

Simplifying
c + 0.25 = -1.973786547

Reorder the terms:
0.25 + c = -1.973786547

Solving
0.25 + c = -1.973786547

Solving for variable 'c'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + c = -1.973786547 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + c = -1.973786547 + -0.25
c = -1.973786547 + -0.25

Combine like terms: -1.973786547 + -0.25 = -2.223786547
c = -2.223786547

Simplifying
c = -2.223786547


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.723786547, -2.223786547}
Solution
c = {1.723786547, -2.223786547}

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