2z^2-10tz+8t^2=0

Solution for 2z^2-10tz+8t^2=0 equation:

Simplifying
2z2 + -10tz + 8t2 = 0

Reorder the terms:
-10tz + 8t2 + 2z2 = 0

Solving
-10tz + 8t2 + 2z2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5tz + 4t2 + z2) = 0

Factor a trinomial.
2((t + -1z)(4t + -1z)) = 0

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

Simplifying
t + -1z = 0

Solving
t + -1z = 0

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

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

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

Simplifying
t = z
Subproblem 2
Set the factor '(4t + -1z)' equal to zero and attempt to solve:

Simplifying
4t + -1z = 0

Solving
4t + -1z = 0

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

Add 'z' to each side of the equation.
4t + -1z + z = 0 + z

Combine like terms: -1z + z = 0
4t + 0 = 0 + z
4t = 0 + z
Remove the zero:
4t = z

Divide each side by '4'.
t = 0.25z

Simplifying
t = 0.25z
Solution
t = {z, 0.25z}