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

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

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

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

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

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

Combine like terms: -2r + 5r = 3r
(-10 + 3r + r2) = 0

Solving
-10 + 3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -1r)(2 + -1r) = 0

Subproblem 1
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
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 = {-5, 2}