(s^2)*(s+1)*(s-2)=0

Solution for (s^2)*(s+1)*(s-2)=0 equation:

Simplifying
(s2)(s + 1)(s + -2) = 0

Reorder the terms:
s2(1 + s)(s + -2) = 0

Reorder the terms:
s2(1 + s)(-2 + s) = 0

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

Combine like terms: 1s + -2s = -1s
s2(-2 + -1s + s2) = 0
(-2 * s2 + -1s * s2 + s2 * s2) = 0
(-2s2 + -1s3 + s4) = 0

Solving
-2s2 + -1s3 + s4 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), 's2'.
s2(-2 + -1s + s2) = 0

Factor a trinomial.
s2((-1 + -1s)(2 + -1s)) = 0

Subproblem 1
Set the factor 's2' equal to zero and attempt to solve:

Simplifying
s2 = 0

Solving
s2 = 0

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

Simplifying
s2 = 0

Take the square root of each side:
s = {0}
Subproblem 2
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 3
Set the factor '(2 + -1s)' equal to zero and attempt to solve:

Simplifying
2 + -1s = 0

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

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

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

Divide each side by '-1'.
s = 2

Simplifying
s = 2
Solution
s = {0, -1, 2}