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

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

Subproblem 1
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
Subproblem 2
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 = {-1, 0.6666666667}