t^2-3tf-10f^2=0

Solution for t^2-3tf-10f^2=0 equation:

Simplifying
t2 + -3tf + -10f2 = 0

Reorder the terms:
-3ft + -10f2 + t2 = 0

Solving
-3ft + -10f2 + t2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-2f + -1t)(5f + -1t) = 0

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

Simplifying
-2f + -1t = 0

Solving
-2f + -1t = 0

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

Add 't' to each side of the equation.
-2f + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-2f + 0 = 0 + t
-2f = 0 + t
Remove the zero:
-2f = t

Divide each side by '-2'.
f = -0.5t

Simplifying
f = -0.5t
Subproblem 2
Set the factor '(5f + -1t)' equal to zero and attempt to solve:

Simplifying
5f + -1t = 0

Solving
5f + -1t = 0

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

Add 't' to each side of the equation.
5f + -1t + t = 0 + t

Combine like terms: -1t + t = 0
5f + 0 = 0 + t
5f = 0 + t
Remove the zero:
5f = t

Divide each side by '5'.
f = 0.2t

Simplifying
f = 0.2t
Solution
f = {-0.5t, 0.2t}