f=fm(9n-1)

Solution for f=fm(9n-1) equation:

Simplifying
f = fm(9n + -1)

Reorder the terms:
f = fm(-1 + 9n)
f = (-1 * fm + 9n * fm)
f = (-1fm + 9fmn)

Solving
f = -1fm + 9fmn

Solving for variable 'f'.

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

Add 'fm' to each side of the equation.
f + fm = -1fm + fm + 9fmn

Combine like terms: -1fm + fm = 0
f + fm = 0 + 9fmn
f + fm = 9fmn

Add '-9fmn' to each side of the equation.
f + fm + -9fmn = 9fmn + -9fmn

Combine like terms: 9fmn + -9fmn = 0
f + fm + -9fmn = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(1 + m + -9mn) = 0

Subproblem 1
Set the factor 'f' equal to zero and attempt to solve:

Simplifying
f = 0

Solving
f = 0

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

Simplifying
f = 0
Subproblem 2
Set the factor '(1 + m + -9mn)' equal to zero and attempt to solve:

Simplifying
1 + m + -9mn = 0

Solving
1 + m + -9mn = 0

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

Add '-1' to each side of the equation.
1 + m + -1 + -9mn = 0 + -1

Reorder the terms:
1 + -1 + m + -9mn = 0 + -1

Combine like terms: 1 + -1 = 0
0 + m + -9mn = 0 + -1
m + -9mn = 0 + -1

Combine like terms: 0 + -1 = -1
m + -9mn = -1

Add '-1m' to each side of the equation.
m + -1m + -9mn = -1 + -1m

Combine like terms: m + -1m = 0
0 + -9mn = -1 + -1m
-9mn = -1 + -1m

Add '9mn' to each side of the equation.
-9mn + 9mn = -1 + -1m + 9mn

Combine like terms: -9mn + 9mn = 0
0 = -1 + -1m + 9mn

Simplifying
0 = -1 + -1m + 9mn

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
f = {0}