10s^2-13st-3t^2=0

Solution for 10s^2-13st-3t^2=0 equation:

Simplifying
10s2 + -13st + -3t2 = 0

Reorder the terms:
-13st + 10s2 + -3t2 = 0

Solving
-13st + 10s2 + -3t2 = 0

Solving for variable 's'.

Factor a trinomial.
(2s + -3t)(5s + t) = 0

Subproblem 1
Set the factor '(2s + -3t)' equal to zero and attempt to solve:

Simplifying
2s + -3t = 0

Solving
2s + -3t = 0

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

Add '3t' to each side of the equation.
2s + -3t + 3t = 0 + 3t

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

Divide each side by '2'.
s = 1.5t

Simplifying
s = 1.5t
Subproblem 2
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
Solution
s = {1.5t, -0.2t}