24f^2+72f+54=0

Solution for 24f^2+72f+54=0 equation:

Simplifying
24f2 + 72f + 54 = 0

Reorder the terms:
54 + 72f + 24f2 = 0

Solving
54 + 72f + 24f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + 12f + 4f2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {-1.5, -1.5}