Question

How do you solve `5r^2 - 44r + 120 = -30 + 11r` by factoring?

Answer 1

`r = 5, 6`

Explanation:

`5 r^2 - 44 r + 120 = -30 + 11 r`
`=> 5 r^2 - 55 r + 150 = 0` (Adding `30 - 11 r` to both sides)
`=> r^2 - 11 r + 30 = 0` (Dividing by 5)
`=> r^2 - 5 r - 6 r + 30 = 0` (Noting that `30 = 5 * 6`, and that `5 + 6 = 11`)
`=> r ( r - 5 ) - 6 ( r - 5 ) = 0`
`=> ( r - 5 ) ( r - 6 ) = 0`
`=> r = 5` or `r = 6`