t^2+tu-2u^2=0

Solution for t^2+tu-2u^2=0 equation:

Simplifying
t2 + tu + -2u2 = 0

Reorder the terms:
tu + t2 + -2u2 = 0

Solving
tu + t2 + -2u2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -1u)(t + 2u) = 0

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

Simplifying
t + -1u = 0

Solving
t + -1u = 0

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

Add 'u' to each side of the equation.
t + -1u + u = 0 + u

Combine like terms: -1u + u = 0
t + 0 = 0 + u
t = 0 + u
Remove the zero:
t = u

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

Simplifying
t + 2u = 0

Solving
t + 2u = 0

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

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

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

Simplifying
t = -2u
Solution
t = {u, -2u}