6c(c-8)=8(2-c)

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Solution for 6c(c-8)=8(2-c) equation:


Simplifying
6c(c + -8) = 8(2 + -1c)

Reorder the terms:
6c(-8 + c) = 8(2 + -1c)
(-8 * 6c + c * 6c) = 8(2 + -1c)
(-48c + 6c2) = 8(2 + -1c)
-48c + 6c2 = (2 * 8 + -1c * 8)
-48c + 6c2 = (16 + -8c)

Solving
-48c + 6c2 = 16 + -8c

Solving for variable 'c'.

Reorder the terms:
-16 + -48c + 8c + 6c2 = 16 + -8c + -16 + 8c

Combine like terms: -48c + 8c = -40c
-16 + -40c + 6c2 = 16 + -8c + -16 + 8c

Reorder the terms:
-16 + -40c + 6c2 = 16 + -16 + -8c + 8c

Combine like terms: 16 + -16 = 0
-16 + -40c + 6c2 = 0 + -8c + 8c
-16 + -40c + 6c2 = -8c + 8c

Combine like terms: -8c + 8c = 0
-16 + -40c + 6c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -20c + 3c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -20c + 3c2)' equal to zero and attempt to solve:

Simplifying
-8 + -20c + 3c2 = 0

Solving
-8 + -20c + 3c2 = 0

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

Divide each side by '3'.
-2.666666667 + -6.666666667c + c2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -6.666666667c + 2.666666667 + c2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -6.666666667c + c2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -6.666666667c + c2 = 0 + 2.666666667
-6.666666667c + c2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-6.666666667c + c2 = 2.666666667

The c term is -6.666666667c.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667c + 11.11111112 + c2 = 2.666666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667c + c2 = 2.666666667 + 11.11111112

Combine like terms: 2.666666667 + 11.11111112 = 13.777777787
11.11111112 + -6.666666667c + c2 = 13.777777787

Factor a perfect square on the left side:
(c + -3.333333334)(c + -3.333333334) = 13.777777787

Calculate the square root of the right side: 3.71184291

Break this problem into two subproblems by setting 
(c + -3.333333334) equal to 3.71184291 and -3.71184291.


Subproblem 1
c + -3.333333334 = 3.71184291

Simplifying
c + -3.333333334 = 3.71184291

Reorder the terms:
-3.333333334 + c = 3.71184291

Solving
-3.333333334 + c = 3.71184291

Solving for variable 'c'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + c = 3.71184291 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + c = 3.71184291 + 3.333333334
c = 3.71184291 + 3.333333334

Combine like terms: 3.71184291 + 3.333333334 = 7.045176244
c = 7.045176244

Simplifying
c = 7.045176244


Subproblem 2
c + -3.333333334 = -3.71184291

Simplifying
c + -3.333333334 = -3.71184291

Reorder the terms:
-3.333333334 + c = -3.71184291

Solving
-3.333333334 + c = -3.71184291

Solving for variable 'c'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + c = -3.71184291 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + c = -3.71184291 + 3.333333334
c = -3.71184291 + 3.333333334

Combine like terms: -3.71184291 + 3.333333334 = -0.378509576
c = -0.378509576

Simplifying
c = -0.378509576


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {7.045176244, -0.378509576}
Solution
c = {7.045176244, -0.378509576}

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