6s^2-30s+24=0

Solution for 6s^2-30s+24=0 equation:

Simplifying
6s2 + -30s + 24 = 0

Reorder the terms:
24 + -30s + 6s2 = 0

Solving
24 + -30s + 6s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -5s + s2) = 0

Factor a trinomial.
6((1 + -1s)(4 + -1s)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1s)' equal to zero and attempt to solve:

Simplifying
1 + -1s = 0

Solving
1 + -1s = 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 + -1s = 0 + -1

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

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

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

Simplifying
s = 1
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 = {1, 4}