4c^2-4c-120=0

Solution for 4c^2-4c-120=0 equation:

Simplifying
4c2 + -4c + -120 = 0

Reorder the terms:
-120 + -4c + 4c2 = 0

Solving
-120 + -4c + 4c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + -1c + c2) = 0

Factor a trinomial.
4((-5 + -1c)(6 + -1c)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -1c)' equal to zero and attempt to solve:

Simplifying
-5 + -1c = 0

Solving
-5 + -1c = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1c = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1c = 0 + 5
-1c = 0 + 5

Combine like terms: 0 + 5 = 5
-1c = 5

Divide each side by '-1'.
c = -5

Simplifying
c = -5
Subproblem 2
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
Solution
c = {-5, 6}