f(x)-xf(x)-x^2f(x)=x

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Solution for f(x)-xf(x)-x^2f(x)=x equation: 


Simplifying
f(x) + -1xf(x) + -1x2f(x) = x

Multiply f * x
fx + -1xf(x) + -1x2f(x) = x

Multiply fx * x
fx + -1fx2 + -1x2f(x) = x

Multiply fx2 * x
fx + -1fx2 + -1fx3 = x

Solving
fx + -1fx2 + -1fx3 = x

Solving for variable 'f'.

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

Combine like terms: x + -1x = 0
fx + -1fx2 + -1fx3 + -1x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(f + -1fx + -1fx2 + -1) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(f + -1fx + -1fx2 + -1)' equal to zero and attempt to solve:

Simplifying
f + -1fx + -1fx2 + -1 = 0

Reorder the terms:
-1 + f + -1fx + -1fx2 = 0

Solving
-1 + f + -1fx + -1fx2 = 0

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

Add '1' to each side of the equation.
-1 + f + -1fx + 1 + -1fx2 = 0 + 1

Reorder the terms:
-1 + 1 + f + -1fx + -1fx2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + f + -1fx + -1fx2 = 0 + 1
f + -1fx + -1fx2 = 0 + 1

Combine like terms: 0 + 1 = 1
f + -1fx + -1fx2 = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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