(r+5)(r-3)=0

Solution for (r+5)(r-3)=0 equation:

Simplifying
(r + 5)(r + -3) = 0

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

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

Multiply (5 + r) * (-3 + r)
(5(-3 + r) + r(-3 + r)) = 0
((-3 * 5 + r * 5) + r(-3 + r)) = 0
((-15 + 5r) + r(-3 + r)) = 0
(-15 + 5r + (-3 * r + r * r)) = 0
(-15 + 5r + (-3r + r2)) = 0

Combine like terms: 5r + -3r = 2r
(-15 + 2r + r2) = 0

Solving
-15 + 2r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -1r)(3 + -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 '(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 = {-5, 3}