(6s-24)(24s-6)=0

Solution for (6s-24)(24s-6)=0 equation:

Simplifying
(6s + -24)(24s + -6) = 0

Reorder the terms:
(-24 + 6s)(24s + -6) = 0

Reorder the terms:
(-24 + 6s)(-6 + 24s) = 0

Multiply (-24 + 6s) * (-6 + 24s)
(-24(-6 + 24s) + 6s * (-6 + 24s)) = 0
((-6 * -24 + 24s * -24) + 6s * (-6 + 24s)) = 0
((144 + -576s) + 6s * (-6 + 24s)) = 0
(144 + -576s + (-6 * 6s + 24s * 6s)) = 0
(144 + -576s + (-36s + 144s2)) = 0

Combine like terms: -576s + -36s = -612s
(144 + -612s + 144s2) = 0

Solving
144 + -612s + 144s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '36'.
36(4 + -17s + 4s2) = 0

Factor a trinomial.
36((1 + -4s)(4 + -1s)) = 0

Ignore the factor 36.
Subproblem 1
Set the factor '(1 + -4s)' equal to zero and attempt to solve:

Simplifying
1 + -4s = 0

Solving
1 + -4s = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4s = 0 + -1
-4s = 0 + -1

Combine like terms: 0 + -1 = -1
-4s = -1

Divide each side by '-4'.
s = 0.25

Simplifying
s = 0.25
Subproblem 2
Set the factor '(4 + -1s)' equal to zero and attempt to solve:

Simplifying
4 + -1s = 0

Solving
4 + -1s = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1s = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1s = 0 + -4
-1s = 0 + -4

Combine like terms: 0 + -4 = -4
-1s = -4

Divide each side by '-1'.
s = 4

Simplifying
s = 4
Solution
s = {0.25, 4}