Question

How do you factor `-x^2+15x-50=0`?

Answer 1

`-x^2+15x-50 = 0`
or, equivalnetly
`(-1)(x^2-15x+50) = 0`

We are looking for two constants: `a` and `b` such that
`a+b= -15`
and
`axxb = 50`

The obvious pair is `(a,b) = (-5,-10)`
gives us
`-x^2+15x-50 = 0`
`-= (-1)(x-5)(x-10) = 0`

Note that it is unusual to be asked to factor an equation; normally we only factor expressions:
`-x^2+15x-50 = (-1)(x-5)(x-10)`

It may be that the intent was to extract
`x-5 = 0`
and
`x-10=0`
as factors of the original equation (check with your instructor).