t^2-2ty-48y^2=0

Solution for t^2-2ty-48y^2=0 equation:

Simplifying
t2 + -2ty + -48y2 = 0

Reorder the terms:
-2ty + t2 + -48y2 = 0

Solving
-2ty + t2 + -48y2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -8y)(t + 6y) = 0

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

Simplifying
t + -8y = 0

Solving
t + -8y = 0

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

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

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

Simplifying
t = 8y
Subproblem 2
Set the factor '(t + 6y)' equal to zero and attempt to solve:

Simplifying
t + 6y = 0

Solving
t + 6y = 0

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

Add '-6y' to each side of the equation.
t + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
t + 0 = 0 + -6y
t = 0 + -6y
Remove the zero:
t = -6y

Simplifying
t = -6y
Solution
t = {8y, -6y}