(9r-2)(r+6)=0

Solution for (9r-2)(r+6)=0 equation:

Simplifying
(9r + -2)(r + 6) = 0

Reorder the terms:
(-2 + 9r)(r + 6) = 0

Reorder the terms:
(-2 + 9r)(6 + r) = 0

Multiply (-2 + 9r) * (6 + r)
(-2(6 + r) + 9r * (6 + r)) = 0
((6 * -2 + r * -2) + 9r * (6 + r)) = 0
((-12 + -2r) + 9r * (6 + r)) = 0
(-12 + -2r + (6 * 9r + r * 9r)) = 0
(-12 + -2r + (54r + 9r2)) = 0

Combine like terms: -2r + 54r = 52r
(-12 + 52r + 9r2) = 0

Solving
-12 + 52r + 9r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -1r)(2 + -9r) = 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 '(2 + -9r)' equal to zero and attempt to solve:

Simplifying
2 + -9r = 0

Solving
2 + -9r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9r = 0 + -2
-9r = 0 + -2

Combine like terms: 0 + -2 = -2
-9r = -2

Divide each side by '-9'.
r = 0.2222222222

Simplifying
r = 0.2222222222
Solution
r = {-6, 0.2222222222}