2s(9s-2)(2s-1)=0

Solution for 2s(9s-2)(2s-1)=0 equation:

Simplifying
2s(9s + -2)(2s + -1) = 0

Reorder the terms:
2s(-2 + 9s)(2s + -1) = 0

Reorder the terms:
2s(-2 + 9s)(-1 + 2s) = 0

Multiply (-2 + 9s) * (-1 + 2s)
2s(-2(-1 + 2s) + 9s * (-1 + 2s)) = 0
2s((-1 * -2 + 2s * -2) + 9s * (-1 + 2s)) = 0
2s((2 + -4s) + 9s * (-1 + 2s)) = 0
2s(2 + -4s + (-1 * 9s + 2s * 9s)) = 0
2s(2 + -4s + (-9s + 18s2)) = 0

Combine like terms: -4s + -9s = -13s
2s(2 + -13s + 18s2) = 0
(2 * 2s + -13s * 2s + 18s2 * 2s) = 0
(4s + -26s2 + 36s3) = 0

Solving
4s + -26s2 + 36s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2s'.
2s(2 + -13s + 18s2) = 0

Factor a trinomial.
2s((2 + -9s)(1 + -2s)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(2 + -9s)' equal to zero and attempt to solve:

Simplifying
2 + -9s = 0

Solving
2 + -9s = 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 + -9s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9s = 0 + -2
-9s = 0 + -2

Combine like terms: 0 + -2 = -2
-9s = -2

Divide each side by '-9'.
s = 0.2222222222

Simplifying
s = 0.2222222222
Subproblem 3
Set the factor '(1 + -2s)' equal to zero and attempt to solve:

Simplifying
1 + -2s = 0

Solving
1 + -2s = 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 + -2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2s = 0 + -1
-2s = 0 + -1

Combine like terms: 0 + -1 = -1
-2s = -1

Divide each side by '-2'.
s = 0.5

Simplifying
s = 0.5
Solution
s = {0, 0.2222222222, 0.5}