(s+t^2)(2s+3t^2)=0

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

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

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

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

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

Combine like terms: 3st2 + 2st2 = 5st2
(5st2 + 2s2 + 3t4) = 0

Solving
5st2 + 2s2 + 3t4 = 0

Solving for variable 's'.

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

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

Simplifying
s + t2 = 0

Solving
s + t2 = 0

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

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

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

Simplifying
s = -1t2
Subproblem 2
Set the factor '(2s + 3t2)' equal to zero and attempt to solve:

Simplifying
2s + 3t2 = 0

Solving
2s + 3t2 = 0

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

Add '-3t2' to each side of the equation.
2s + 3t2 + -3t2 = 0 + -3t2

Combine like terms: 3t2 + -3t2 = 0
2s + 0 = 0 + -3t2
2s = 0 + -3t2
Remove the zero:
2s = -3t2

Divide each side by '2'.
s = -1.5t2

Simplifying
s = -1.5t2
Solution
s = {-1t2, -1.5t2}