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

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

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

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

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

Multiply (-2 + 3r) * (-1 + 2r)
2r(-2(-1 + 2r) + 3r * (-1 + 2r)) = 0
2r((-1 * -2 + 2r * -2) + 3r * (-1 + 2r)) = 0
2r((2 + -4r) + 3r * (-1 + 2r)) = 0
2r(2 + -4r + (-1 * 3r + 2r * 3r)) = 0
2r(2 + -4r + (-3r + 6r2)) = 0

Combine like terms: -4r + -3r = -7r
2r(2 + -7r + 6r2) = 0
(2 * 2r + -7r * 2r + 6r2 * 2r) = 0
(4r + -14r2 + 12r3) = 0

Solving
4r + -14r2 + 12r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(2 + -7r + 6r2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
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
Subproblem 3
Set the factor '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 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 + -3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3r = 0 + -2
-3r = 0 + -2

Combine like terms: 0 + -2 = -2
-3r = -2

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Solution
r = {0, 0.5, 0.6666666667}