27=c(c-6)

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

Simplifying
27 = c(c + -6)

Reorder the terms:
27 = c(-6 + c)
27 = (-6 * c + c * c)
27 = (-6c + c2)

Solving
27 = -6c + c2

Solving for variable 'c'.

Reorder the terms:
27 + 6c + -1c2 = -6c + 6c + c2 + -1c2

Combine like terms: -6c + 6c = 0
27 + 6c + -1c2 = 0 + c2 + -1c2
27 + 6c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
27 + 6c + -1c2 = 0

Factor a trinomial.
(9 + -1c)(3 + c) = 0

Subproblem 1
Set the factor '(9 + -1c)' equal to zero and attempt to solve:

Simplifying
9 + -1c = 0

Solving
9 + -1c = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1c = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1c = 0 + -9
-1c = 0 + -9

Combine like terms: 0 + -9 = -9
-1c = -9

Divide each side by '-1'.
c = 9

Simplifying
c = 9
Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve:

Simplifying
3 + c = 0

Solving
3 + c = 0

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

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

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

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

Simplifying
c = -3
Solution
c = {9, -3}