3f^2-13f-16=0

Solution for 3f^2-13f-16=0 equation:

Simplifying
3f2 + -13f + -16 = 0

Reorder the terms:
-16 + -13f + 3f2 = 0

Solving
-16 + -13f + 3f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -1f)(16 + -3f) = 0

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

Simplifying
-1 + -1f = 0

Solving
-1 + -1f = 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 + -1f = 0 + 1

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

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

Divide each side by '-1'.
f = -1

Simplifying
f = -1
Subproblem 2
Set the factor '(16 + -3f)' equal to zero and attempt to solve:

Simplifying
16 + -3f = 0

Solving
16 + -3f = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3f = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3f = 0 + -16
-3f = 0 + -16

Combine like terms: 0 + -16 = -16
-3f = -16

Divide each side by '-3'.
f = 5.333333333

Simplifying
f = 5.333333333
Solution
f = {-1, 5.333333333}