t^2+10tf+16f^2=

Solution for t^2+10tf+16f^2= equation:

Simplifying
t2 + 10tf + 16f2 = 0

Reorder the terms:
10ft + 16f2 + t2 = 0

Solving
10ft + 16f2 + t2 = 0

Solving for variable 'f'.

Factor a trinomial.
(8f + t)(2f + t) = 0

Subproblem 1
Set the factor '(8f + t)' equal to zero and attempt to solve:

Simplifying
8f + t = 0

Solving
8f + t = 0

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

Add '-1t' to each side of the equation.
8f + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
8f + 0 = 0 + -1t
8f = 0 + -1t
Remove the zero:
8f = -1t

Divide each side by '8'.
f = -0.125t

Simplifying
f = -0.125t
Subproblem 2
Set the factor '(2f + t)' equal to zero and attempt to solve:

Simplifying
2f + t = 0

Solving
2f + t = 0

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

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

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

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

Simplifying
f = -0.5t
Solution
f = {-0.125t, -0.5t}