12f^2+80f+48=0

Solution for 12f^2+80f+48=0 equation:

Simplifying
12f2 + 80f + 48 = 0

Reorder the terms:
48 + 80f + 12f2 = 0

Solving
48 + 80f + 12f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 20f + 3f2) = 0

Factor a trinomial.
4((6 + f)(2 + 3f)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + f)' equal to zero and attempt to solve:

Simplifying
6 + f = 0

Solving
6 + f = 0

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

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

Combine like terms: 6 + -6 = 0
0 + f = 0 + -6
f = 0 + -6

Combine like terms: 0 + -6 = -6
f = -6

Simplifying
f = -6
Subproblem 2
Set the factor '(2 + 3f)' equal to zero and attempt to solve:

Simplifying
2 + 3f = 0

Solving
2 + 3f = 0

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

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

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

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

Divide each side by '3'.
f = -0.6666666667

Simplifying
f = -0.6666666667
Solution
f = {-6, -0.6666666667}