t^2-2ty-35y^2=0

Solution for t^2-2ty-35y^2=0 equation:

Simplifying
t2 + -2ty + -35y2 = 0

Reorder the terms:
-2ty + t2 + -35y2 = 0

Solving
-2ty + t2 + -35y2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -7y)(t + 5y) = 0

Subproblem 1
Set the factor '(t + -7y)' equal to zero and attempt to solve:

Simplifying
t + -7y = 0

Solving
t + -7y = 0

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

Add '7y' to each side of the equation.
t + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
t + 0 = 0 + 7y
t = 0 + 7y
Remove the zero:
t = 7y

Simplifying
t = 7y
Subproblem 2
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
Solution
t = {7y, -5y}