6f^2+27f+30=0

Solution for 6f^2+27f+30=0 equation:

Simplifying
6f2 + 27f + 30 = 0

Reorder the terms:
30 + 27f + 6f2 = 0

Solving
30 + 27f + 6f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 9f + 2f2) = 0

Factor a trinomial.
3((5 + 2f)(2 + f)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 2f)' equal to zero and attempt to solve:

Simplifying
5 + 2f = 0

Solving
5 + 2f = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2f = 0 + -5
2f = 0 + -5

Combine like terms: 0 + -5 = -5
2f = -5

Divide each side by '2'.
f = -2.5

Simplifying
f = -2.5
Subproblem 2
Set the factor '(2 + f)' equal to zero and attempt to solve:

Simplifying
2 + f = 0

Solving
2 + f = 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 + f = 0 + -2

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

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

Simplifying
f = -2
Solution
f = {-2.5, -2}