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

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

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

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

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

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

Combine like terms: -2r + -3r = -5r
0 = (6 + -5r + r2)

Solving
0 = 6 + -5r + r2

Solving for variable 'r'.

Combine like terms: 0 + -6 = -6
-6 + 5r + -1r2 = 6 + -5r + r2 + -6 + 5r + -1r2

Reorder the terms:
-6 + 5r + -1r2 = 6 + -6 + -5r + 5r + r2 + -1r2

Combine like terms: 6 + -6 = 0
-6 + 5r + -1r2 = 0 + -5r + 5r + r2 + -1r2
-6 + 5r + -1r2 = -5r + 5r + r2 + -1r2

Combine like terms: -5r + 5r = 0
-6 + 5r + -1r2 = 0 + r2 + -1r2
-6 + 5r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-6 + 5r + -1r2 = 0

Factor a trinomial.
(-3 + r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-3 + r)' equal to zero and attempt to solve:

Simplifying
-3 + r = 0

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

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

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

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