8r(r+2)(3r-1)=0

Solution for 8r(r+2)(3r-1)=0 equation:

Simplifying
8r(r + 2)(3r + -1) = 0

Reorder the terms:
8r(2 + r)(3r + -1) = 0

Reorder the terms:
8r(2 + r)(-1 + 3r) = 0

Multiply (2 + r) * (-1 + 3r)
8r(2(-1 + 3r) + r(-1 + 3r)) = 0
8r((-1 * 2 + 3r * 2) + r(-1 + 3r)) = 0
8r((-2 + 6r) + r(-1 + 3r)) = 0
8r(-2 + 6r + (-1 * r + 3r * r)) = 0
8r(-2 + 6r + (-1r + 3r2)) = 0

Combine like terms: 6r + -1r = 5r
8r(-2 + 5r + 3r2) = 0
(-2 * 8r + 5r * 8r + 3r2 * 8r) = 0
(-16r + 40r2 + 24r3) = 0

Solving
-16r + 40r2 + 24r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8r'.
8r(-2 + 5r + 3r2) = 0

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

Ignore the factor 8.
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 '(-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
Subproblem 3
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

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

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

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {0, -2, 0.3333333333}