9f^2+12f+4=0

Solution for 9f^2+12f+4=0 equation:

Simplifying
9f2 + 12f + 4 = 0

Reorder the terms:
4 + 12f + 9f2 = 0

Solving
4 + 12f + 9f2 = 0

Solving for variable 'f'.

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

Subproblem 1
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
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 = {-0.6666666667, -0.6666666667}