12f^2-31f+7=0

Solution for 12f^2-31f+7=0 equation:

Simplifying
12f2 + -31f + 7 = 0

Reorder the terms:
7 + -31f + 12f2 = 0

Solving
7 + -31f + 12f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(1 + -4f)(7 + -3f) = 0

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

Simplifying
1 + -4f = 0

Solving
1 + -4f = 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 + -4f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4f = 0 + -1
-4f = 0 + -1

Combine like terms: 0 + -1 = -1
-4f = -1

Divide each side by '-4'.
f = 0.25

Simplifying
f = 0.25
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 = {0.25, 2.333333333}