4c(c-3)6=92

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

Simplifying
4c(c + -3) * 6 = 92

Reorder the terms:
4c(-3 + c) * 6 = 92

Reorder the terms for easier multiplication:
4 * 6c(-3 + c) = 92

Multiply 4 * 6
24c(-3 + c) = 92
(-3 * 24c + c * 24c) = 92
(-72c + 24c2) = 92

Solving
-72c + 24c2 = 92

Solving for variable 'c'.

Reorder the terms:
-92 + -72c + 24c2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + -72c + 24c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + -18c + 6c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-23 + -18c + 6c2)' equal to zero and attempt to solve:

Simplifying
-23 + -18c + 6c2 = 0

Solving
-23 + -18c + 6c2 = 0

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

Divide each side by '6'.
-3.833333333 + -3c + c2 = 0

Move the constant term to the right:

Add '3.833333333' to each side of the equation.
-3.833333333 + -3c + 3.833333333 + c2 = 0 + 3.833333333

Reorder the terms:
-3.833333333 + 3.833333333 + -3c + c2 = 0 + 3.833333333

Combine like terms: -3.833333333 + 3.833333333 = 0.000000000
0.000000000 + -3c + c2 = 0 + 3.833333333
-3c + c2 = 0 + 3.833333333

Combine like terms: 0 + 3.833333333 = 3.833333333
-3c + c2 = 3.833333333

The c term is -3c.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3c + 2.25 + c2 = 3.833333333 + 2.25

Reorder the terms:
2.25 + -3c + c2 = 3.833333333 + 2.25

Combine like terms: 3.833333333 + 2.25 = 6.083333333
2.25 + -3c + c2 = 6.083333333

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = 6.083333333

Calculate the square root of the right side: 2.466441431

Break this problem into two subproblems by setting 
(c + -1.5) equal to 2.466441431 and -2.466441431.

Subproblem 1
c + -1.5 = 2.466441431

Simplifying
c + -1.5 = 2.466441431

Reorder the terms:
-1.5 + c = 2.466441431

Solving
-1.5 + c = 2.466441431

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = 2.466441431 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = 2.466441431 + 1.5
c = 2.466441431 + 1.5

Combine like terms: 2.466441431 + 1.5 = 3.966441431
c = 3.966441431

Simplifying
c = 3.966441431

Subproblem 2
c + -1.5 = -2.466441431

Simplifying
c + -1.5 = -2.466441431

Reorder the terms:
-1.5 + c = -2.466441431

Solving
-1.5 + c = -2.466441431

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = -2.466441431 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = -2.466441431 + 1.5
c = -2.466441431 + 1.5

Combine like terms: -2.466441431 + 1.5 = -0.966441431
c = -0.966441431

Simplifying
c = -0.966441431

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.966441431, -0.966441431}
Solution
c = {3.966441431, -0.966441431}