27=3c(6-2c)

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

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

Solving
27 = 18c + -6c2

Solving for variable 'c'.

Reorder the terms:
27 + -18c + 6c2 = 18c + -18c + -6c2 + 6c2

Combine like terms: 18c + -18c = 0
27 + -18c + 6c2 = 0 + -6c2 + 6c2
27 + -18c + 6c2 = -6c2 + 6c2

Combine like terms: -6c2 + 6c2 = 0
27 + -18c + 6c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -6c + 2c2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + -6c + 2c2)' equal to zero and attempt to solve:

Simplifying
9 + -6c + 2c2 = 0

Solving
9 + -6c + 2c2 = 0

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

Divide each side by '2'.
4.5 + -3c + c2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -3c + -4.5 + c2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -3c + c2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -3c + c2 = 0 + -4.5
-3c + c2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-3c + c2 = -4.5

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 = -4.5 + 2.25

Reorder the terms:
2.25 + -3c + c2 = -4.5 + 2.25

Combine like terms: -4.5 + 2.25 = -2.25
2.25 + -3c + c2 = -2.25

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.