4f^2+12f+9=0

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

Simplifying
4f2 + 12f + 9 = 0

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

Solving
9 + 12f + 4f2 = 0

Solving for variable 'f'.

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

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}