f^2-30f=31

Solution for f^2-30f=31 equation:

Simplifying
f2 + -30f = 31

Reorder the terms:
-30f + f2 = 31

Solving
-30f + f2 = 31

Solving for variable 'f'.

Reorder the terms:
-31 + -30f + f2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + -30f + f2 = 0

Factor a trinomial.
(-1 + -1f)(31 + -1f) = 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 '(31 + -1f)' equal to zero and attempt to solve:

Simplifying
31 + -1f = 0

Solving
31 + -1f = 0

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

Add '-31' to each side of the equation.
31 + -31 + -1f = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -1f = 0 + -31
-1f = 0 + -31

Combine like terms: 0 + -31 = -31
-1f = -31

Divide each side by '-1'.
f = 31

Simplifying
f = 31
Solution
f = {-1, 31}