3s^2+7st+2t^2=0

Solution for 3s^2+7st+2t^2=0 equation:

Simplifying
3s2 + 7st + 2t2 = 0

Reorder the terms:
7st + 3s2 + 2t2 = 0

Solving
7st + 3s2 + 2t2 = 0

Solving for variable 's'.

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

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

Simplifying
3s + t = 0

Solving
3s + t = 0

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

Add '-1t' to each side of the equation.
3s + t + -1t = 0 + -1t

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

Divide each side by '3'.
s = -0.3333333333t

Simplifying
s = -0.3333333333t
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 = {-0.3333333333t, -2t}