-8r^3+31r^2-21r=0

Solution for -8r^3+31r^2-21r=0 equation:

Simplifying
-8r3 + 31r2 + -21r = 0

Reorder the terms:
-21r + 31r2 + -8r3 = 0

Solving
-21r + 31r2 + -8r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-21 + 31r + -8r2) = 0

Factor a trinomial.
r((-3 + r)(7 + -8r)) = 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 '(-3 + r)' equal to zero and attempt to solve:

Simplifying
-3 + r = 0

Solving
-3 + r = 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 + r = 0 + 3

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

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

Simplifying
r = 3
Subproblem 3
Set the factor '(7 + -8r)' equal to zero and attempt to solve:

Simplifying
7 + -8r = 0

Solving
7 + -8r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8r = 0 + -7
-8r = 0 + -7

Combine like terms: 0 + -7 = -7
-8r = -7

Divide each side by '-8'.
r = 0.875

Simplifying
r = 0.875
Solution
r = {0, 3, 0.875}