25r^3-16r=0

Solution for 25r^3-16r=0 equation:

Simplifying
25r3 + -16r = 0

Reorder the terms:
-16r + 25r3 = 0

Solving
-16r + 25r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-16 + 25r2) = 0

Factor a difference between two squares.
r((4 + 5r)(-4 + 5r)) = 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 '(4 + 5r)' equal to zero and attempt to solve:

Simplifying
4 + 5r = 0

Solving
4 + 5r = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5r = 0 + -4
5r = 0 + -4

Combine like terms: 0 + -4 = -4
5r = -4

Divide each side by '5'.
r = -0.8

Simplifying
r = -0.8
Subproblem 3
Set the factor '(-4 + 5r)' equal to zero and attempt to solve:

Simplifying
-4 + 5r = 0

Solving
-4 + 5r = 0

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

Add '4' to each side of the equation.
-4 + 4 + 5r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5r = 0 + 4
5r = 0 + 4

Combine like terms: 0 + 4 = 4
5r = 4

Divide each side by '5'.
r = 0.8

Simplifying
r = 0.8
Solution
r = {0, -0.8, 0.8}