(4f^2-3)+11f=0

Solution for (4f^2-3)+11f=0 equation:

Simplifying
(4f2 + -3) + 11f = 0

Reorder the terms:
(-3 + 4f2) + 11f = 0

Remove parenthesis around (-3 + 4f2)
-3 + 4f2 + 11f = 0

Reorder the terms:
-3 + 11f + 4f2 = 0

Solving
-3 + 11f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-3 + -1f)(1 + -4f) = 0

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

Simplifying
-3 + -1f = 0

Solving
-3 + -1f = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1f = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1f = 0 + 3
-1f = 0 + 3

Combine like terms: 0 + 3 = 3
-1f = 3

Divide each side by '-1'.
f = -3

Simplifying
f = -3
Subproblem 2
Set the factor '(1 + -4f)' equal to zero and attempt to solve:

Simplifying
1 + -4f = 0

Solving
1 + -4f = 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 + -4f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4f = 0 + -1
-4f = 0 + -1

Combine like terms: 0 + -1 = -1
-4f = -1

Divide each side by '-4'.
f = 0.25

Simplifying
f = 0.25
Solution
f = {-3, 0.25}