-5r^2+25r^3+10r^2=0

Solution for -5r^2+25r^3+10r^2=0 equation:

Simplifying
-5r2 + 25r3 + 10r2 = 0

Reorder the terms:
-5r2 + 10r2 + 25r3 = 0

Combine like terms: -5r2 + 10r2 = 5r2
5r2 + 25r3 = 0

Solving
5r2 + 25r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r2'.
5r2(1 + 5r) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}
Subproblem 2
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 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 + 5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5r = 0 + -1
5r = 0 + -1

Combine like terms: 0 + -1 = -1
5r = -1

Divide each side by '5'.
r = -0.2

Simplifying
r = -0.2
Solution
r = {0, -0.2}