3f^2-7f-10=0

Solution for 3f^2-7f-10=0 equation:

Simplifying
3f2 + -7f + -10 = 0

Reorder the terms:
-10 + -7f + 3f2 = 0

Solving
-10 + -7f + 3f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -1f)(10 + -3f) = 0

Subproblem 1
Set the factor '(-1 + -1f)' equal to zero and attempt to solve:

Simplifying
-1 + -1f = 0

Solving
-1 + -1f = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1f = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1f = 0 + 1
-1f = 0 + 1

Combine like terms: 0 + 1 = 1
-1f = 1

Divide each side by '-1'.
f = -1

Simplifying
f = -1
Subproblem 2
Set the factor '(10 + -3f)' equal to zero and attempt to solve:

Simplifying
10 + -3f = 0

Solving
10 + -3f = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3f = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3f = 0 + -10
-3f = 0 + -10

Combine like terms: 0 + -10 = -10
-3f = -10

Divide each side by '-3'.
f = 3.333333333

Simplifying
f = 3.333333333
Solution
f = {-1, 3.333333333}