(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 = -5r
(6 + -5r + r2) = 0

Solving
6 + -5r + 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}