s^2-5st-24t^2=0

Solution for s^2-5st-24t^2=0 equation:

Simplifying
s2 + -5st + -24t2 = 0

Reorder the terms:
-5st + s2 + -24t2 = 0

Solving
-5st + s2 + -24t2 = 0

Solving for variable 's'.

Factor a trinomial.
(s + -8t)(s + 3t) = 0

Subproblem 1
Set the factor '(s + -8t)' equal to zero and attempt to solve:

Simplifying
s + -8t = 0

Solving
s + -8t = 0

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

Add '8t' to each side of the equation.
s + -8t + 8t = 0 + 8t

Combine like terms: -8t + 8t = 0
s + 0 = 0 + 8t
s = 0 + 8t
Remove the zero:
s = 8t

Simplifying
s = 8t
Subproblem 2
Set the factor '(s + 3t)' equal to zero and attempt to solve:

Simplifying
s + 3t = 0

Solving
s + 3t = 0

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

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

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

Simplifying
s = -3t
Solution
s = {8t, -3t}