(3s+t^2)(s+2t^2)=

Solution for (3s+t^2)(s+2t^2)= equation:

Simplifying
(3s + t2)(s + 2t2) = 0

Multiply (3s + t2) * (s + 2t2)
(3s * (s + 2t2) + t2(s + 2t2)) = 0
((s * 3s + 2t2 * 3s) + t2(s + 2t2)) = 0

Reorder the terms:
((6st2 + 3s2) + t2(s + 2t2)) = 0
((6st2 + 3s2) + t2(s + 2t2)) = 0
(6st2 + 3s2 + (s * t2 + 2t2 * t2)) = 0
(6st2 + 3s2 + (st2 + 2t4)) = 0

Reorder the terms:
(6st2 + st2 + 3s2 + 2t4) = 0

Combine like terms: 6st2 + st2 = 7st2
(7st2 + 3s2 + 2t4) = 0

Solving
7st2 + 3s2 + 2t4 = 0

Solving for variable 's'.

Factor a trinomial.
(3s + t2)(s + 2t2) = 0

Subproblem 1
Set the factor '(3s + t2)' equal to zero and attempt to solve:

Simplifying
3s + t2 = 0

Solving
3s + t2 = 0

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

Add '-1t2' to each side of the equation.
3s + t2 + -1t2 = 0 + -1t2

Combine like terms: t2 + -1t2 = 0
3s + 0 = 0 + -1t2
3s = 0 + -1t2
Remove the zero:
3s = -1t2

Divide each side by '3'.
s = -0.3333333333t2

Simplifying
s = -0.3333333333t2
Subproblem 2
Set the factor '(s + 2t2)' equal to zero and attempt to solve:

Simplifying
s + 2t2 = 0

Solving
s + 2t2 = 0

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

Add '-2t2' to each side of the equation.
s + 2t2 + -2t2 = 0 + -2t2

Combine like terms: 2t2 + -2t2 = 0
s + 0 = 0 + -2t2
s = 0 + -2t2
Remove the zero:
s = -2t2

Simplifying
s = -2t2
Solution
s = {-0.3333333333t2, -2t2}