c^2-3c-54=0

Solution for c^2-3c-54=0 equation:

Simplifying
c2 + -3c + -54 = 0

Reorder the terms:
-54 + -3c + c2 = 0

Solving
-54 + -3c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-6 + -1c)(9 + -1c) = 0

Subproblem 1
Set the factor '(-6 + -1c)' equal to zero and attempt to solve:

Simplifying
-6 + -1c = 0

Solving
-6 + -1c = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1c = 0 + 6

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

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

Divide each side by '-1'.
c = -6

Simplifying
c = -6
Subproblem 2
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
Solution
c = {-6, 9}