t^2-8tz+15z^2=0

Solution for t^2-8tz+15z^2=0 equation:

Simplifying
t2 + -8tz + 15z2 = 0

Reorder the terms:
-8tz + t2 + 15z2 = 0

Solving
-8tz + t2 + 15z2 = 0

Solving for variable 't'.

Factor a trinomial.
(t + -5z)(t + -3z) = 0

Subproblem 1
Set the factor '(t + -5z)' equal to zero and attempt to solve:

Simplifying
t + -5z = 0

Solving
t + -5z = 0

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

Add '5z' to each side of the equation.
t + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
t + 0 = 0 + 5z
t = 0 + 5z
Remove the zero:
t = 5z

Simplifying
t = 5z
Subproblem 2
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
Solution
t = {5z, 3z}