(r-5)(r-2)=0

Solution for (r-5)(r-2)=0 equation:

Simplifying
(r + -5)(r + -2) = 0

Reorder the terms:
(-5 + r)(r + -2) = 0

Reorder the terms:
(-5 + r)(-2 + r) = 0

Multiply (-5 + r) * (-2 + r)
(-5(-2 + r) + r(-2 + r)) = 0
((-2 * -5 + r * -5) + r(-2 + r)) = 0
((10 + -5r) + r(-2 + r)) = 0
(10 + -5r + (-2 * r + r * r)) = 0
(10 + -5r + (-2r + r2)) = 0

Combine like terms: -5r + -2r = -7r
(10 + -7r + r2) = 0

Solving
10 + -7r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + -1r)(5 + -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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

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

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

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {2, 5}