[6-2c]3c-3=27

Solution for [6-2c]3c-3=27 equation:

Simplifying
[6 + -2c] * 3c + -3 = 27

Reorder the terms for easier multiplication:
3c[6 + -2c] + -3 = 27
[6 * 3c + -2c * 3c] + -3 = 27
[18c + -6c2] + -3 = 27

Reorder the terms:
-3 + 18c + -6c2 = 27

Solving
-3 + 18c + -6c2 = 27

Solving for variable 'c'.

Reorder the terms:
-3 + -27 + 18c + -6c2 = 27 + -27

Combine like terms: -3 + -27 = -30
-30 + 18c + -6c2 = 27 + -27

Combine like terms: 27 + -27 = 0
-30 + 18c + -6c2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 3c + -1c2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + 3c + -1c2)' equal to zero and attempt to solve:

Simplifying
-5 + 3c + -1c2 = 0

Solving
-5 + 3c + -1c2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -3c + c2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -3c + -5 + c2 = 0 + -5

Reorder the terms:
5 + -5 + -3c + c2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3c + c2 = 0 + -5
-3c + c2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3c + c2 = -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 = -5 + 2.25

Reorder the terms:
2.25 + -3c + c2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + -3c + c2 = -2.75

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = -2.75

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.