5r^3-10r=

Solution for 5r^3-10r= equation:

Simplifying
5r3 + -10r = 0

Reorder the terms:
-10r + 5r3 = 0

Solving
-10r + 5r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(-2 + r2) = 0

Ignore the factor 5.
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 '(-2 + r2)' equal to zero and attempt to solve:

Simplifying
-2 + r2 = 0

Solving
-2 + r2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + r2 = 0 + 2
r2 = 0 + 2

Combine like terms: 0 + 2 = 2
r2 = 2

Simplifying
r2 = 2

Take the square root of each side:
r = {-1.414213562, 1.414213562}
Solution
r = {0, -1.414213562, 1.414213562}