4c^2+12c-72=0

Solution for 4c^2+12c-72=0 equation:

Simplifying
4c2 + 12c + -72 = 0

Reorder the terms:
-72 + 12c + 4c2 = 0

Solving
-72 + 12c + 4c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 3c + c2) = 0

Factor a trinomial.
4((-6 + -1c)(3 + -1c)) = 0

Ignore the factor 4.
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 '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

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

Combine like terms: 3 + -3 = 0
0 + -1c = 0 + -3
-1c = 0 + -3

Combine like terms: 0 + -3 = -3
-1c = -3

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {-6, 3}