t^2+3tf-28f^2=

Solution for t^2+3tf-28f^2= equation:

Simplifying
t2 + 3tf + -28f2 = 0

Reorder the terms:
3ft + -28f2 + t2 = 0

Solving
3ft + -28f2 + t2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-7f + -1t)(4f + -1t) = 0

Subproblem 1
Set the factor '(-7f + -1t)' equal to zero and attempt to solve:

Simplifying
-7f + -1t = 0

Solving
-7f + -1t = 0

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

Add 't' to each side of the equation.
-7f + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-7f + 0 = 0 + t
-7f = 0 + t
Remove the zero:
-7f = t

Divide each side by '-7'.
f = -0.1428571429t

Simplifying
f = -0.1428571429t
Subproblem 2
Set the factor '(4f + -1t)' equal to zero and attempt to solve:

Simplifying
4f + -1t = 0

Solving
4f + -1t = 0

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

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

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

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

Simplifying
f = 0.25t
Solution
f = {-0.1428571429t, 0.25t}