2r^3+16r^2=40r

Solution for 2r^3+16r^2=40r equation:

Simplifying
2r3 + 16r2 = 40r

Reorder the terms:
16r2 + 2r3 = 40r

Solving
16r2 + 2r3 = 40r

Solving for variable 'r'.

Reorder the terms:
-40r + 16r2 + 2r3 = 40r + -40r

Combine like terms: 40r + -40r = 0
-40r + 16r2 + 2r3 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-20 + 8r + r2) = 0

Factor a trinomial.
2r((-10 + -1r)(2 + -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 '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0, -10, 2}