3f^2-4f-7=0

Solution for 3f^2-4f-7=0 equation:

Simplifying
3f2 + -4f + -7 = 0

Reorder the terms:
-7 + -4f + 3f2 = 0

Solving
-7 + -4f + 3f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -1f)(7 + -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 '(7 + -3f)' equal to zero and attempt to solve:

Simplifying
7 + -3f = 0

Solving
7 + -3f = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3f = 0 + -7
-3f = 0 + -7

Combine like terms: 0 + -7 = -7
-3f = -7

Divide each side by '-3'.
f = 2.333333333

Simplifying
f = 2.333333333
Solution
f = {-1, 2.333333333}