2c^2-52c-54=0

Solution for 2c^2-52c-54=0 equation:

Simplifying
2c2 + -52c + -54 = 0

Reorder the terms:
-54 + -52c + 2c2 = 0

Solving
-54 + -52c + 2c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -26c + c2) = 0

Factor a trinomial.
2((-1 + -1c)(27 + -1c)) = 0

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

Simplifying
-1 + -1c = 0

Solving
-1 + -1c = 0

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

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

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

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

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

Simplifying
c = -1
Subproblem 2
Set the factor '(27 + -1c)' equal to zero and attempt to solve:

Simplifying
27 + -1c = 0

Solving
27 + -1c = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1c = 0 + -27

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

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

Divide each side by '-1'.
c = 27

Simplifying
c = 27
Solution
c = {-1, 27}