(s-3)(s+2)=0

Solution for (s-3)(s+2)=0 equation:

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

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

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

Multiply (-3 + s) * (2 + s)
(-3(2 + s) + s(2 + s)) = 0
((2 * -3 + s * -3) + s(2 + s)) = 0
((-6 + -3s) + s(2 + s)) = 0
(-6 + -3s + (2 * s + s * s)) = 0
(-6 + -3s + (2s + s2)) = 0

Combine like terms: -3s + 2s = -1s
(-6 + -1s + s2) = 0

Solving
-6 + -1s + s2 = 0

Solving for variable 's'.

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

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

Simplifying
-2 + -1s = 0

Solving
-2 + -1s = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1s = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1s = 0 + 2
-1s = 0 + 2

Combine like terms: 0 + 2 = 2
-1s = 2

Divide each side by '-1'.
s = -2

Simplifying
s = -2
Subproblem 2
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
Solution
s = {-2, 3}