9r^3-1r=0

Solution for 9r^3-1r=0 equation:

Simplifying
9r3 + -1r = 0

Reorder the terms:
-1r + 9r3 = 0

Solving
-1r + 9r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-1 + 9r2) = 0

Factor a difference between two squares.
r((1 + 3r)(-1 + 3r)) = 0

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 3
Set the factor '(-1 + 3r)' equal to zero and attempt to solve:

Simplifying
-1 + 3r = 0

Solving
-1 + 3r = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3r = 0 + 1
3r = 0 + 1

Combine like terms: 0 + 1 = 1
3r = 1

Divide each side by '3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {0, -0.3333333333, 0.3333333333}