4f^2-5f-6=0

Solution for 4f^2-5f-6=0 equation:

Simplifying
4f2 + -5f + -6 = 0

Reorder the terms:
-6 + -5f + 4f2 = 0

Solving
-6 + -5f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-3 + -4f)(2 + -1f) = 0

Subproblem 1
Set the factor '(-3 + -4f)' equal to zero and attempt to solve:

Simplifying
-3 + -4f = 0

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

Combine like terms: -3 + 3 = 0
0 + -4f = 0 + 3
-4f = 0 + 3

Combine like terms: 0 + 3 = 3
-4f = 3

Divide each side by '-4'.
f = -0.75

Simplifying
f = -0.75
Subproblem 2
Set the factor '(2 + -1f)' equal to zero and attempt to solve:

Simplifying
2 + -1f = 0

Solving
2 + -1f = 0

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

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

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

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

Divide each side by '-1'.
f = 2

Simplifying
f = 2
Solution
f = {-0.75, 2}