5s^2+6st+t^2=0

Solution for 5s^2+6st+t^2=0 equation:

Simplifying
5s2 + 6st + t2 = 0

Reorder the terms:
6st + 5s2 + t2 = 0

Solving
6st + 5s2 + t2 = 0

Solving for variable 's'.

Factor a trinomial.
(5s + t)(s + t) = 0

Subproblem 1
Set the factor '(5s + t)' equal to zero and attempt to solve:

Simplifying
5s + t = 0

Solving
5s + t = 0

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

Add '-1t' to each side of the equation.
5s + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
5s + 0 = 0 + -1t
5s = 0 + -1t
Remove the zero:
5s = -1t

Divide each side by '5'.
s = -0.2t

Simplifying
s = -0.2t
Subproblem 2
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
Solution
s = {-0.2t, -1t}