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

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

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

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

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

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

Combine like terms: -2s + 30s = 28s
(-12 + 28s + 5s2) = 0

Solving
-12 + 28s + 5s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-6 + -1s)(2 + -5s) = 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 '(2 + -5s)' equal to zero and attempt to solve:

Simplifying
2 + -5s = 0

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

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

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

Divide each side by '-5'.
s = 0.4

Simplifying
s = 0.4
Solution
s = {-6, 0.4}