5f^2+18f+9=0

Solution for 5f^2+18f+9=0 equation:

Simplifying
5f2 + 18f + 9 = 0

Reorder the terms:
9 + 18f + 5f2 = 0

Solving
9 + 18f + 5f2 = 0

Solving for variable 'f'.

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

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 + 5f)' equal to zero and attempt to solve:

Simplifying
3 + 5f = 0

Solving
3 + 5f = 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 + 5f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5f = 0 + -3
5f = 0 + -3

Combine like terms: 0 + -3 = -3
5f = -3

Divide each side by '5'.
f = -0.6

Simplifying
f = -0.6
Solution
f = {-3, -0.6}