8r^4-24r^3+10r^2=0

Solution for 8r^4-24r^3+10r^2=0 equation:

Simplifying
8r4 + -24r3 + 10r2 = 0

Reorder the terms:
10r2 + -24r3 + 8r4 = 0

Solving
10r2 + -24r3 + 8r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r2'.
2r2(5 + -12r + 4r2) = 0

Factor a trinomial.
2r2((1 + -2r)(5 + -2r)) = 0

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 3
Set the factor '(5 + -2r)' equal to zero and attempt to solve:

Simplifying
5 + -2r = 0

Solving
5 + -2r = 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 + -2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2r = 0 + -5
-2r = 0 + -5

Combine like terms: 0 + -5 = -5
-2r = -5

Divide each side by '-2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {0, 0.5, 2.5}