2F^2-42F+40=0

Solution for 2F^2-42F+40=0 equation:

Simplifying
2F2 + -42F + 40 = 0

Reorder the terms:
40 + -42F + 2F2 = 0

Solving
40 + -42F + 2F2 = 0

Solving for variable 'F'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -21F + F2) = 0

Factor a trinomial.
2((1 + -1F)(20 + -1F)) = 0

Ignore the factor 2.
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 '(20 + -1F)' equal to zero and attempt to solve:

Simplifying
20 + -1F = 0

Solving
20 + -1F = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1F = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1F = 0 + -20
-1F = 0 + -20

Combine like terms: 0 + -20 = -20
-1F = -20

Divide each side by '-1'.
F = 20

Simplifying
F = 20
Solution
F = {1, 20}