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

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

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

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

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

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

Combine like terms: -3r + 2r = -1r
(-6 + -1r + r2) = 0

Solving
-6 + -1r + r2 = 0

Solving for variable 'r'.

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

Simplifying
3 + -1r = 0

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

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-2, 3}