(r+3)(r+6)=

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

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

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

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

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

Combine like terms: 3r + 6r = 9r
(18 + 9r + r2) = 0

Solving
18 + 9r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + r)(3 + r) = 0

Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 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 + r = 0 + -6

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

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

Simplifying
r = -6
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 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 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Solution
r = {-6, -3}