4f^2-80f+76=0

Solution for 4f^2-80f+76=0 equation:

Simplifying
4f2 + -80f + 76 = 0

Reorder the terms:
76 + -80f + 4f2 = 0

Solving
76 + -80f + 4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(19 + -20f + f2) = 0

Factor a trinomial.
4((1 + -1f)(19 + -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 '(19 + -1f)' equal to zero and attempt to solve:

Simplifying
19 + -1f = 0

Solving
19 + -1f = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1f = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1f = 0 + -19
-1f = 0 + -19

Combine like terms: 0 + -19 = -19
-1f = -19

Divide each side by '-1'.
f = 19

Simplifying
f = 19
Solution
f = {1, 19}