4f^2+4f-48=0

Solution for 4f^2+4f-48=0 equation:

Simplifying
4f2 + 4f + -48 = 0

Reorder the terms:
-48 + 4f + 4f2 = 0

Solving
-48 + 4f + 4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + f + f2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -1f)' equal to zero and attempt to solve:

Simplifying
-4 + -1f = 0

Solving
-4 + -1f = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1f = 0 + 4

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

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

Divide each side by '-1'.
f = -4

Simplifying
f = -4
Subproblem 2
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
Solution
f = {-4, 3}