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

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

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

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

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

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

Combine like terms: 6r + -5r = 1r
5(-30 + 1r + r2) = 0
(-30 * 5 + 1r * 5 + r2 * 5) = 0
(-150 + 5r + 5r2) = 0

Solving
-150 + 5r + 5r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-30 + r + r2) = 0

Factor a trinomial.
5((-6 + -1r)(5 + -1r)) = 0

Ignore the factor 5.
Subproblem 1
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 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
Solution
r = {-6, 5}