Form an equation whose roots are 1/2 and -1/3. i would appreciate shown work, but whatever you like

==> When any factor of a number is zero, the number itself is zero.

==> When any factor of an expression is zero, the whole expression is zero.

So we can construct an equation that says an "expression is equal to zero",
if we make the expression out of 2 factors ... one that's zero when x=1/2,
and the other one that's zero when x= -1/3 .  Clever ? ! ?

OK.  One factor ==>   (x - 1/2) .   That's zero when  x= 1/2 .

The other factor ==>  (x + 1/3) .   That's zero when  x = -1/3 .

Multiply the factors, and you have the expression:  (x-1/2) (x+1/3) .

Proclaim that the expression is equal to zero:

                         (x - 1/2) · (x + 1/3)  =  0   .

Voila !  Now you have an equation that's only a true statement
IF  x = 1/2  OR  x = -1/3 .

In other words,  1/2 and -1/3 are the solutions, or roots, of the equation.

If U wanna FOIL it out and get another way to write it
without parentheses, go ahead:

                     x² - 1/6x - 1/6  =  0 

If you wanna multiply each side by 6 and get another way
to write it without fractions, go ahead:

                           6x² - x - 1  =  0

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.