8(c-9)=6(2c-12)4c

Solution for 8(c-9)=6(2c-12)4c equation:

Simplifying
8(c + -9) = 6(2c + -12) * 4c

Reorder the terms:
8(-9 + c) = 6(2c + -12) * 4c
(-9 * 8 + c * 8) = 6(2c + -12) * 4c
(-72 + 8c) = 6(2c + -12) * 4c

Reorder the terms:
-72 + 8c = 6(-12 + 2c) * 4c

Reorder the terms for easier multiplication:
-72 + 8c = 6 * 4c(-12 + 2c)

Multiply 6 * 4
-72 + 8c = 24c(-12 + 2c)
-72 + 8c = (-12 * 24c + 2c * 24c)
-72 + 8c = (-288c + 48c2)

Solving
-72 + 8c = -288c + 48c2

Solving for variable 'c'.

Combine like terms: 8c + 288c = 296c
-72 + 296c + -48c2 = -288c + 48c2 + 288c + -48c2

Reorder the terms:
-72 + 296c + -48c2 = -288c + 288c + 48c2 + -48c2

Combine like terms: -288c + 288c = 0
-72 + 296c + -48c2 = 0 + 48c2 + -48c2
-72 + 296c + -48c2 = 48c2 + -48c2

Combine like terms: 48c2 + -48c2 = 0
-72 + 296c + -48c2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-9 + 37c + -6c2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-9 + 37c + -6c2)' equal to zero and attempt to solve:

Simplifying
-9 + 37c + -6c2 = 0

Solving
-9 + 37c + -6c2 = 0

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

Divide each side by '-6'.
1.5 + -6.166666667c + c2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -6.166666667c + -1.5 + c2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -6.166666667c + c2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -6.166666667c + c2 = 0 + -1.5
-6.166666667c + c2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-6.166666667c + c2 = -1.5

The c term is -6.166666667c.  Take half its coefficient (-3.083333334).
Square it (9.506944449) and add it to both sides.

Add '9.506944449' to each side of the equation.
-6.166666667c + 9.506944449 + c2 = -1.5 + 9.506944449

Reorder the terms:
9.506944449 + -6.166666667c + c2 = -1.5 + 9.506944449

Combine like terms: -1.5 + 9.506944449 = 8.006944449
9.506944449 + -6.166666667c + c2 = 8.006944449

Factor a perfect square on the left side:
(c + -3.083333334)(c + -3.083333334) = 8.006944449

Calculate the square root of the right side: 2.829654475

Break this problem into two subproblems by setting 
(c + -3.083333334) equal to 2.829654475 and -2.829654475.

Subproblem 1
c + -3.083333334 = 2.829654475

Simplifying
c + -3.083333334 = 2.829654475

Reorder the terms:
-3.083333334 + c = 2.829654475

Solving
-3.083333334 + c = 2.829654475

Solving for variable 'c'.

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

Add '3.083333334' to each side of the equation.
-3.083333334 + 3.083333334 + c = 2.829654475 + 3.083333334

Combine like terms: -3.083333334 + 3.083333334 = 0.000000000
0.000000000 + c = 2.829654475 + 3.083333334
c = 2.829654475 + 3.083333334

Combine like terms: 2.829654475 + 3.083333334 = 5.912987809
c = 5.912987809

Simplifying
c = 5.912987809

Subproblem 2
c + -3.083333334 = -2.829654475

Simplifying
c + -3.083333334 = -2.829654475

Reorder the terms:
-3.083333334 + c = -2.829654475

Solving
-3.083333334 + c = -2.829654475

Solving for variable 'c'.

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

Add '3.083333334' to each side of the equation.
-3.083333334 + 3.083333334 + c = -2.829654475 + 3.083333334

Combine like terms: -3.083333334 + 3.083333334 = 0.000000000
0.000000000 + c = -2.829654475 + 3.083333334
c = -2.829654475 + 3.083333334

Combine like terms: -2.829654475 + 3.083333334 = 0.253678859
c = 0.253678859

Simplifying
c = 0.253678859

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {5.912987809, 0.253678859}
Solution
c = {5.912987809, 0.253678859}