(s-3t)(s-2t)=0

Solution for (s-3t)(s-2t)=0 equation:

Simplifying
(s + -3t)(s + -2t) = 0

Multiply (s + -3t) * (s + -2t)
(s(s + -2t) + -3t * (s + -2t)) = 0
((s * s + -2t * s) + -3t * (s + -2t)) = 0

Reorder the terms:
((-2st + s2) + -3t * (s + -2t)) = 0
((-2st + s2) + -3t * (s + -2t)) = 0
(-2st + s2 + (s * -3t + -2t * -3t)) = 0
(-2st + s2 + (-3st + 6t2)) = 0

Reorder the terms:
(-2st + -3st + s2 + 6t2) = 0

Combine like terms: -2st + -3st = -5st
(-5st + s2 + 6t2) = 0

Solving
-5st + s2 + 6t2 = 0

Solving for variable 's'.

Factor a trinomial.
(s + -3t)(s + -2t) = 0

Subproblem 1
Set the factor '(s + -3t)' equal to zero and attempt to solve:

Simplifying
s + -3t = 0

Solving
s + -3t = 0

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

Add '3t' to each side of the equation.
s + -3t + 3t = 0 + 3t

Combine like terms: -3t + 3t = 0
s + 0 = 0 + 3t
s = 0 + 3t
Remove the zero:
s = 3t

Simplifying
s = 3t
Subproblem 2
Set the factor '(s + -2t)' equal to zero and attempt to solve:

Simplifying
s + -2t = 0

Solving
s + -2t = 0

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

Add '2t' to each side of the equation.
s + -2t + 2t = 0 + 2t

Combine like terms: -2t + 2t = 0
s + 0 = 0 + 2t
s = 0 + 2t
Remove the zero:
s = 2t

Simplifying
s = 2t
Solution
s = {3t, 2t}