(3s+6t)(s+t)=

Solution for (3s+6t)(s+t)= equation:

Simplifying
(3s + 6t)(s + t) = 0

Multiply (3s + 6t) * (s + t)
(3s * (s + t) + 6t * (s + t)) = 0
((s * 3s + t * 3s) + 6t * (s + t)) = 0

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

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

Combine like terms: 3st + 6st = 9st
(9st + 3s2 + 6t2) = 0

Solving
9st + 3s2 + 6t2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3st + s2 + 2t2) = 0

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

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

Simplifying
s + t = 0

Solving
s + t = 0

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

Add '-1t' to each side of the equation.
s + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
s + 0 = 0 + -1t
s = 0 + -1t
Remove the zero:
s = -1t

Simplifying
s = -1t
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 = {-1t, -2t}