r(r+5)(r-6)=0

Solution for r(r+5)(r-6)=0 equation:

Simplifying
r(r + 5)(r + -6) = 0

Reorder the terms:
r(5 + r)(r + -6) = 0

Reorder the terms:
r(5 + r)(-6 + r) = 0

Multiply (5 + r) * (-6 + r)
r(5(-6 + r) + r(-6 + r)) = 0
r((-6 * 5 + r * 5) + r(-6 + r)) = 0
r((-30 + 5r) + r(-6 + r)) = 0
r(-30 + 5r + (-6 * r + r * r)) = 0
r(-30 + 5r + (-6r + r2)) = 0

Combine like terms: 5r + -6r = -1r
r(-30 + -1r + r2) = 0
(-30 * r + -1r * r + r2 * r) = 0
(-30r + -1r2 + r3) = 0

Solving
-30r + -1r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-30 + -1r + r2) = 0

Factor a trinomial.
r((-5 + -1r)(6 + -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 '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 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 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 3
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
Solution
r = {0, -5, 6}