t^2+7tv-18v^2=0

Solution for t^2+7tv-18v^2=0 equation:

Simplifying
t2 + 7tv + -18v2 = 0

Reorder the terms:
7tv + t2 + -18v2 = 0

Solving
7tv + t2 + -18v2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -2v)(t + 9v) = 0

Subproblem 1
Set the factor '(t + -2v)' equal to zero and attempt to solve:

Simplifying
t + -2v = 0

Solving
t + -2v = 0

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

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

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

Simplifying
t = 2v
Subproblem 2
Set the factor '(t + 9v)' equal to zero and attempt to solve:

Simplifying
t + 9v = 0

Solving
t + 9v = 0

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

Add '-9v' to each side of the equation.
t + 9v + -9v = 0 + -9v

Combine like terms: 9v + -9v = 0
t + 0 = 0 + -9v
t = 0 + -9v
Remove the zero:
t = -9v

Simplifying
t = -9v
Solution
t = {2v, -9v}