r(r-3)(r+6)=0

Solution for r(r-3)(r+6)=0 equation:

Simplifying
r(r + -3)(r + 6) = 0

Reorder the terms:
r(-3 + r)(r + 6) = 0

Reorder the terms:
r(-3 + r)(6 + r) = 0

Multiply (-3 + r) * (6 + r)
r(-3(6 + r) + r(6 + r)) = 0
r((6 * -3 + r * -3) + r(6 + r)) = 0
r((-18 + -3r) + r(6 + r)) = 0
r(-18 + -3r + (6 * r + r * r)) = 0
r(-18 + -3r + (6r + r2)) = 0

Combine like terms: -3r + 6r = 3r
r(-18 + 3r + r2) = 0
(-18 * r + 3r * r + r2 * r) = 0
(-18r + 3r2 + r3) = 0

Solving
-18r + 3r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-18 + 3r + r2) = 0

Factor a trinomial.
r((-6 + -1r)(3 + -1r)) = 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 '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
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, -6, 3}