4f^2+33f+35=0

Solution for 4f^2+33f+35=0 equation:

Simplifying
4f2 + 33f + 35 = 0

Reorder the terms:
35 + 33f + 4f2 = 0

Solving
35 + 33f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(7 + f)(5 + 4f) = 0

Subproblem 1
Set the factor '(7 + f)' equal to zero and attempt to solve:

Simplifying
7 + f = 0

Solving
7 + f = 0

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

Add '-7' to each side of the equation.
7 + -7 + f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + f = 0 + -7
f = 0 + -7

Combine like terms: 0 + -7 = -7
f = -7

Simplifying
f = -7
Subproblem 2
Set the factor '(5 + 4f)' equal to zero and attempt to solve:

Simplifying
5 + 4f = 0

Solving
5 + 4f = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4f = 0 + -5
4f = 0 + -5

Combine like terms: 0 + -5 = -5
4f = -5

Divide each side by '4'.
f = -1.25

Simplifying
f = -1.25
Solution
f = {-7, -1.25}