t^2-2ty-15y^2=0

Solution for t^2-2ty-15y^2=0 equation:

Simplifying
t2 + -2ty + -15y2 = 0

Reorder the terms:
-2ty + t2 + -15y2 = 0

Solving
-2ty + t2 + -15y2 = 0

Solving for variable 't'.

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

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

Simplifying
t + -5y = 0

Solving
t + -5y = 0

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

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

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

Simplifying
t = 5y
Subproblem 2
Set the factor '(t + 3y)' equal to zero and attempt to solve:

Simplifying
t + 3y = 0

Solving
t + 3y = 0

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

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

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

Simplifying
t = -3y
Solution
t = {5y, -3y}