t^2-8tz+12z^2=0

Solution for t^2-8tz+12z^2=0 equation:

Simplifying
t2 + -8tz + 12z2 = 0

Reorder the terms:
-8tz + t2 + 12z2 = 0

Solving
-8tz + t2 + 12z2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -6z)(t + -2z) = 0

Subproblem 1
Set the factor '(t + -6z)' equal to zero and attempt to solve:

Simplifying
t + -6z = 0

Solving
t + -6z = 0

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

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

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

Simplifying
t = 6z
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 = {6z, 2z}