(r+9)(r-6)=0

Solution for (r+9)(r-6)=0 equation:

Simplifying
(r + 9)(r + -6) = 0

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

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

Multiply (9 + r) * (-6 + r)
(9(-6 + r) + r(-6 + r)) = 0
((-6 * 9 + r * 9) + r(-6 + r)) = 0
((-54 + 9r) + r(-6 + r)) = 0
(-54 + 9r + (-6 * r + r * r)) = 0
(-54 + 9r + (-6r + r2)) = 0

Combine like terms: 9r + -6r = 3r
(-54 + 3r + r2) = 0

Solving
-54 + 3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-9 + -1r)' equal to zero and attempt to solve:

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
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
Solution
r = {-9, 6}