25r^3-120r^2+135r=

Solution for 25r^3-120r^2+135r= equation:

Simplifying
25r3 + -120r2 + 135r = 0

Reorder the terms:
135r + -120r2 + 25r3 = 0

Solving
135r + -120r2 + 25r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(27 + -24r + 5r2) = 0

Factor a trinomial.
5r((9 + -5r)(3 + -1r)) = 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 '(9 + -5r)' equal to zero and attempt to solve:

Simplifying
9 + -5r = 0

Solving
9 + -5r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5r = 0 + -9
-5r = 0 + -9

Combine like terms: 0 + -9 = -9
-5r = -9

Divide each side by '-5'.
r = 1.8

Simplifying
r = 1.8
Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0, 1.8, 3}