(r+6)(r-15)=0

Solution for (r+6)(r-15)=0 equation:

Simplifying
(r + 6)(r + -15) = 0

Reorder the terms:
(6 + r)(r + -15) = 0

Reorder the terms:
(6 + r)(-15 + r) = 0

Multiply (6 + r) * (-15 + r)
(6(-15 + r) + r(-15 + r)) = 0
((-15 * 6 + r * 6) + r(-15 + r)) = 0
((-90 + 6r) + r(-15 + r)) = 0
(-90 + 6r + (-15 * r + r * r)) = 0
(-90 + 6r + (-15r + r2)) = 0

Combine like terms: 6r + -15r = -9r
(-90 + -9r + r2) = 0

Solving
-90 + -9r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -1r)(15 + -1r) = 0

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 '(15 + -1r)' equal to zero and attempt to solve:

Simplifying
15 + -1r = 0

Solving
15 + -1r = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1r = 0 + -15
-1r = 0 + -15

Combine like terms: 0 + -15 = -15
-1r = -15

Divide each side by '-1'.
r = 15

Simplifying
r = 15
Solution
r = {-6, 15}