(2s-5)(s+6)=0

Solution for (2s-5)(s+6)=0 equation:

Simplifying
(2s + -5)(s + 6) = 0

Reorder the terms:
(-5 + 2s)(s + 6) = 0

Reorder the terms:
(-5 + 2s)(6 + s) = 0

Multiply (-5 + 2s) * (6 + s)
(-5(6 + s) + 2s * (6 + s)) = 0
((6 * -5 + s * -5) + 2s * (6 + s)) = 0
((-30 + -5s) + 2s * (6 + s)) = 0
(-30 + -5s + (6 * 2s + s * 2s)) = 0
(-30 + -5s + (12s + 2s2)) = 0

Combine like terms: -5s + 12s = 7s
(-30 + 7s + 2s2) = 0

Solving
-30 + 7s + 2s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-6 + -1s)(5 + -2s) = 0

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

Simplifying
5 + -2s = 0

Solving
5 + -2s = 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 + -2s = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2s = 0 + -5
-2s = 0 + -5

Combine like terms: 0 + -5 = -5
-2s = -5

Divide each side by '-2'.
s = 2.5

Simplifying
s = 2.5
Solution
s = {-6, 2.5}