4f^2-16f-9=0

Solution for 4f^2-16f-9=0 equation:

Simplifying
4f2 + -16f + -9 = 0

Reorder the terms:
-9 + -16f + 4f2 = 0

Solving
-9 + -16f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -2f)(9 + -2f) = 0

Subproblem 1
Set the factor '(-1 + -2f)' equal to zero and attempt to solve:

Simplifying
-1 + -2f = 0

Solving
-1 + -2f = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2f = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2f = 0 + 1
-2f = 0 + 1

Combine like terms: 0 + 1 = 1
-2f = 1

Divide each side by '-2'.
f = -0.5

Simplifying
f = -0.5
Subproblem 2
Set the factor '(9 + -2f)' equal to zero and attempt to solve:

Simplifying
9 + -2f = 0

Solving
9 + -2f = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2f = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2f = 0 + -9
-2f = 0 + -9

Combine like terms: 0 + -9 = -9
-2f = -9

Divide each side by '-2'.
f = 4.5

Simplifying
f = 4.5
Solution
f = {-0.5, 4.5}