6f^2-75f-39=0

Solution for 6f^2-75f-39=0 equation:

Simplifying
6f2 + -75f + -39 = 0

Reorder the terms:
-39 + -75f + 6f2 = 0

Solving
-39 + -75f + 6f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + -25f + 2f2) = 0

Factor a trinomial.
3((-1 + -2f)(13 + -1f)) = 0

Ignore the factor 3.
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 '(13 + -1f)' equal to zero and attempt to solve:

Simplifying
13 + -1f = 0

Solving
13 + -1f = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1f = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1f = 0 + -13
-1f = 0 + -13

Combine like terms: 0 + -13 = -13
-1f = -13

Divide each side by '-1'.
f = 13

Simplifying
f = 13
Solution
f = {-0.5, 13}