(s+3)(s-6)=0

Solution for (s+3)(s-6)=0 equation:

Simplifying
(s + 3)(s + -6) = 0

Reorder the terms:
(3 + s)(s + -6) = 0

Reorder the terms:
(3 + s)(-6 + s) = 0

Multiply (3 + s) * (-6 + s)
(3(-6 + s) + s(-6 + s)) = 0
((-6 * 3 + s * 3) + s(-6 + s)) = 0
((-18 + 3s) + s(-6 + s)) = 0
(-18 + 3s + (-6 * s + s * s)) = 0
(-18 + 3s + (-6s + s2)) = 0

Combine like terms: 3s + -6s = -3s
(-18 + -3s + s2) = 0

Solving
-18 + -3s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-3 + -1s)(6 + -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 '(6 + -1s)' equal to zero and attempt to solve:

Simplifying
6 + -1s = 0

Solving
6 + -1s = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1s = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1s = 0 + -6
-1s = 0 + -6

Combine like terms: 0 + -6 = -6
-1s = -6

Divide each side by '-1'.
s = 6

Simplifying
s = 6
Solution
s = {-3, 6}