6(3r-1)(2r+1)=0

Solution for 6(3r-1)(2r+1)=0 equation:

Simplifying
6(3r + -1)(2r + 1) = 0

Reorder the terms:
6(-1 + 3r)(2r + 1) = 0

Reorder the terms:
6(-1 + 3r)(1 + 2r) = 0

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

Combine like terms: -2r + 3r = 1r
6(-1 + 1r + 6r2) = 0
(-1 * 6 + 1r * 6 + 6r2 * 6) = 0
(-6 + 6r + 36r2) = 0

Solving
-6 + 6r + 36r2 = 0

Solving for variable 'r'.

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

Factor a trinomial.
6((-1 + -2r)(1 + -3r)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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
Solution
r = {-0.5, 0.3333333333}