4f^2-4f-8=0

Solution for 4f^2-4f-8=0 equation:

Simplifying
4f2 + -4f + -8 = 0

Reorder the terms:
-8 + -4f + 4f2 = 0

Solving
-8 + -4f + 4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1f + f2) = 0

Factor a trinomial.
4((-1 + -1f)(2 + -1f)) = 0

Ignore the factor 4.
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 '(2 + -1f)' equal to zero and attempt to solve:

Simplifying
2 + -1f = 0

Solving
2 + -1f = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1f = 0 + -2

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

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

Divide each side by '-1'.
f = 2

Simplifying
f = 2
Solution
f = {-1, 2}