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

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

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

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

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

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

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

Solving
-2 + -1r + 3r2 = 0

Solving for variable 'r'.

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {-0.6666666667, 1}