10r^3=250r

Solution for 10r^3=250r equation:

Simplifying
10r3 = 250r

Solving
10r3 = 250r

Solving for variable 'r'.

Reorder the terms:
-250r + 10r3 = 250r + -250r

Combine like terms: 250r + -250r = 0
-250r + 10r3 = 0

Factor out the Greatest Common Factor (GCF), '10r'.
10r(-25 + r2) = 0

Factor a difference between two squares.
10r((5 + r)(-5 + r)) = 0

Ignore the factor 10.
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 '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 0

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

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

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

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

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

Simplifying
-5 + r = 0

Solving
-5 + r = 0

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

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

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

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

Simplifying
r = 5
Solution
r = {0, -5, 5}