2r^3+10r^2=48r

Solution for 2r^3+10r^2=48r equation:

Simplifying
2r3 + 10r2 = 48r

Reorder the terms:
10r2 + 2r3 = 48r

Solving
10r2 + 2r3 = 48r

Solving for variable 'r'.

Reorder the terms:
-48r + 10r2 + 2r3 = 48r + -48r

Combine like terms: 48r + -48r = 0
-48r + 10r2 + 2r3 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-24 + 5r + r2) = 0

Factor a trinomial.
2r((-8 + -1r)(3 + -1r)) = 0

Ignore the factor 2.
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 '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -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, -8, 3}