16f^2+72f+72=0

Solution for 16f^2+72f+72=0 equation:

Simplifying
16f2 + 72f + 72 = 0

Reorder the terms:
72 + 72f + 16f2 = 0

Solving
72 + 72f + 16f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '8'.
8(9 + 9f + 2f2) = 0

Factor a trinomial.
8((3 + f)(3 + 2f)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + f)' equal to zero and attempt to solve:

Simplifying
3 + f = 0

Solving
3 + f = 0

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

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

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

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

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

Simplifying
3 + 2f = 0

Solving
3 + 2f = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2f = 0 + -3
2f = 0 + -3

Combine like terms: 0 + -3 = -3
2f = -3

Divide each side by '2'.
f = -1.5

Simplifying
f = -1.5
Solution
f = {-3, -1.5}