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

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

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

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

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

Multiply (-5 + s) * (3 + s)
(-5(3 + s) + s(3 + s)) = 0
((3 * -5 + s * -5) + s(3 + s)) = 0
((-15 + -5s) + s(3 + s)) = 0
(-15 + -5s + (3 * s + s * s)) = 0
(-15 + -5s + (3s + s2)) = 0

Combine like terms: -5s + 3s = -2s
(-15 + -2s + s2) = 0

Solving
-15 + -2s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-3 + -1s)(5 + -1s) = 0

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

Simplifying
-3 + -1s = 0

Solving
-3 + -1s = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1s = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1s = 0 + 3
-1s = 0 + 3

Combine like terms: 0 + 3 = 3
-1s = 3

Divide each side by '-1'.
s = -3

Simplifying
s = -3
Subproblem 2
Set the factor '(5 + -1s)' equal to zero and attempt to solve:

Simplifying
5 + -1s = 0

Solving
5 + -1s = 0

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

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

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

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

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

Simplifying
s = 5
Solution
s = {-3, 5}