f(0)=x^5-x^3

Solution for f(0)=x^5-x^3 equation:

Simplifying
f(0) = x5 + -1x3

Reorder the terms for easier multiplication:
0f = x5 + -1x3

Anything times zero is zero.
0f = x5 + -1x3

Reorder the terms:
0 = -1x3 + x5

Solving
0 = -1x3 + x5

Solving for variable 'x'.
Remove the zero:
x3 + -1x5 = -1x3 + x5 + x3 + -1x5

Reorder the terms:
x3 + -1x5 = -1x3 + x3 + x5 + -1x5

Combine like terms: -1x3 + x3 = 0
x3 + -1x5 = 0 + x5 + -1x5
x3 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
x3 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(1 + -1x2) = 0

Factor a difference between two squares.
x3((1 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1, 1}