t^2+8tf+15f^2=0

Solution for t^2+8tf+15f^2=0 equation:

Simplifying
t2 + 8tf + 15f2 = 0

Reorder the terms:
8ft + 15f2 + t2 = 0

Solving
8ft + 15f2 + t2 = 0

Solving for variable 'f'.

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

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

Simplifying
5f + t = 0

Solving
5f + t = 0

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

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

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

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

Simplifying
f = -0.2t
Subproblem 2
Set the factor '(3f + t)' equal to zero and attempt to solve:

Simplifying
3f + t = 0

Solving
3f + t = 0

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

Add '-1t' to each side of the equation.
3f + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
3f + 0 = 0 + -1t
3f = 0 + -1t
Remove the zero:
3f = -1t

Divide each side by '3'.
f = -0.3333333333t

Simplifying
f = -0.3333333333t
Solution
f = {-0.2t, -0.3333333333t}