t^2-tz-6z^2=0

Solution for t^2-tz-6z^2=0 equation:

Simplifying
t2 + -1tz + -6z2 = 0

Reorder the terms:
-1tz + t2 + -6z2 = 0

Solving
-1tz + t2 + -6z2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -3z)(t + 2z) = 0

Subproblem 1
Set the factor '(t + -3z)' equal to zero and attempt to solve:

Simplifying
t + -3z = 0

Solving
t + -3z = 0

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

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

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

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

Simplifying
t + 2z = 0

Solving
t + 2z = 0

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

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

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

Simplifying
t = -2z
Solution
t = {3z, -2z}