(9r+3)(2r-1)=0

Solution for (9r+3)(2r-1)=0 equation:

Simplifying
(9r + 3)(2r + -1) = 0

Reorder the terms:
(3 + 9r)(2r + -1) = 0

Reorder the terms:
(3 + 9r)(-1 + 2r) = 0

Multiply (3 + 9r) * (-1 + 2r)
(3(-1 + 2r) + 9r * (-1 + 2r)) = 0
((-1 * 3 + 2r * 3) + 9r * (-1 + 2r)) = 0
((-3 + 6r) + 9r * (-1 + 2r)) = 0
(-3 + 6r + (-1 * 9r + 2r * 9r)) = 0
(-3 + 6r + (-9r + 18r2)) = 0

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

Solving
-3 + -3r + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -1r + 6r2) = 0

Factor a trinomial.
3((-1 + -3r)(1 + -2r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -3r)' equal to zero and attempt to solve:

Simplifying
-1 + -3r = 0

Solving
-1 + -3r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3r = 0 + 1
-3r = 0 + 1

Combine like terms: 0 + 1 = 1
-3r = 1

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {-0.3333333333, 0.5}