12f^2-f-6=0

Solution for 12f^2-f-6=0 equation:

Simplifying
12f2 + -1f + -6 = 0

Reorder the terms:
-6 + -1f + 12f2 = 0

Solving
-6 + -1f + 12f2 = 0

Solving for variable 'f'.

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

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

Simplifying
-2 + -3f = 0

Solving
-2 + -3f = 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 + -3f = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3f = 0 + 2
-3f = 0 + 2

Combine like terms: 0 + 2 = 2
-3f = 2

Divide each side by '-3'.
f = -0.6666666667

Simplifying
f = -0.6666666667
Subproblem 2
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
Solution
f = {-0.6666666667, 0.75}