27=3c-3c(6-2c)

Solution for 27=3c-3c(6-2c) equation:

Simplifying
27 = 3c + -3c(6 + -2c)
27 = 3c + (6 * -3c + -2c * -3c)
27 = 3c + (-18c + 6c2)

Combine like terms: 3c + -18c = -15c
27 = -15c + 6c2

Solving
27 = -15c + 6c2

Solving for variable 'c'.

Reorder the terms:
27 + 15c + -6c2 = -15c + 15c + 6c2 + -6c2

Combine like terms: -15c + 15c = 0
27 + 15c + -6c2 = 0 + 6c2 + -6c2
27 + 15c + -6c2 = 6c2 + -6c2

Combine like terms: 6c2 + -6c2 = 0
27 + 15c + -6c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 5c + -2c2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + 5c + -2c2)' equal to zero and attempt to solve:

Simplifying
9 + 5c + -2c2 = 0

Solving
9 + 5c + -2c2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4.5 + -2.5c + c2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -2.5c + 4.5 + c2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -2.5c + c2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -2.5c + c2 = 0 + 4.5
-2.5c + c2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-2.5c + c2 = 4.5

The c term is -2.5c.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5c + 1.5625 + c2 = 4.5 + 1.5625

Reorder the terms:
1.5625 + -2.5c + c2 = 4.5 + 1.5625

Combine like terms: 4.5 + 1.5625 = 6.0625
1.5625 + -2.5c + c2 = 6.0625

Factor a perfect square on the left side:
(c + -1.25)(c + -1.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(c + -1.25) equal to 2.46221445 and -2.46221445.

Subproblem 1
c + -1.25 = 2.46221445

Simplifying
c + -1.25 = 2.46221445

Reorder the terms:
-1.25 + c = 2.46221445

Solving
-1.25 + c = 2.46221445

Solving for variable 'c'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + c = 2.46221445 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + c = 2.46221445 + 1.25
c = 2.46221445 + 1.25

Combine like terms: 2.46221445 + 1.25 = 3.71221445
c = 3.71221445

Simplifying
c = 3.71221445

Subproblem 2
c + -1.25 = -2.46221445

Simplifying
c + -1.25 = -2.46221445

Reorder the terms:
-1.25 + c = -2.46221445

Solving
-1.25 + c = -2.46221445

Solving for variable 'c'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + c = -2.46221445 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + c = -2.46221445 + 1.25
c = -2.46221445 + 1.25

Combine like terms: -2.46221445 + 1.25 = -1.21221445
c = -1.21221445

Simplifying
c = -1.21221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.71221445, -1.21221445}
Solution
c = {3.71221445, -1.21221445}