(3r+7)(r+6)=0

Solution for (3r+7)(r+6)=0 equation:

Simplifying
(3r + 7)(r + 6) = 0

Reorder the terms:
(7 + 3r)(r + 6) = 0

Reorder the terms:
(7 + 3r)(6 + r) = 0

Multiply (7 + 3r) * (6 + r)
(7(6 + r) + 3r * (6 + r)) = 0
((6 * 7 + r * 7) + 3r * (6 + r)) = 0
((42 + 7r) + 3r * (6 + r)) = 0
(42 + 7r + (6 * 3r + r * 3r)) = 0
(42 + 7r + (18r + 3r2)) = 0

Combine like terms: 7r + 18r = 25r
(42 + 25r + 3r2) = 0

Solving
42 + 25r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + r)(7 + 3r) = 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 '(7 + 3r)' equal to zero and attempt to solve:

Simplifying
7 + 3r = 0

Solving
7 + 3r = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3r = 0 + -7
3r = 0 + -7

Combine like terms: 0 + -7 = -7
3r = -7

Divide each side by '3'.
r = -2.333333333

Simplifying
r = -2.333333333
Solution
r = {-6, -2.333333333}