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

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

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

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

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

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

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

Solving
-2 + 1r + r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-2 + -1r = 0

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

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
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 = {-2, 1}