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

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

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

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

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

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

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

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

Solving for variable 'r'.

Factor a trinomial.
(-1 + -1r)(3 + -2r) = 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 '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2r = 0 + -3

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

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

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-1, 1.5}