2f^2+23f+11=0

Solution for 2f^2+23f+11=0 equation:

Simplifying
2f2 + 23f + 11 = 0

Reorder the terms:
11 + 23f + 2f2 = 0

Solving
11 + 23f + 2f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(11 + f)(1 + 2f) = 0

Subproblem 1
Set the factor '(11 + f)' equal to zero and attempt to solve:

Simplifying
11 + f = 0

Solving
11 + f = 0

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

Add '-11' to each side of the equation.
11 + -11 + f = 0 + -11

Combine like terms: 11 + -11 = 0
0 + f = 0 + -11
f = 0 + -11

Combine like terms: 0 + -11 = -11
f = -11

Simplifying
f = -11
Subproblem 2
Set the factor '(1 + 2f)' equal to zero and attempt to solve:

Simplifying
1 + 2f = 0

Solving
1 + 2f = 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 + 2f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2f = 0 + -1
2f = 0 + -1

Combine like terms: 0 + -1 = -1
2f = -1

Divide each side by '2'.
f = -0.5

Simplifying
f = -0.5
Solution
f = {-11, -0.5}