Factor the following quadratics completely

2r^2 + 5r - 42

Check if splitting the middle term is possible.

List factors of -84

1 * -84

-1 * 84

2 * -42

-2 * 42

3 * -28

-3 * 28

4 * -21

-4 * 21

6 * -14

-6 * 14

7 * -12

-7 * 12 (these digits satisfy the criteria.)

Split the middle term.

2r^2 + 12r - 7r - 42

Factor by grouping.

2r(r + 6) - 7(r + 6)

Rearrange.

(2r - 7)(r + 6)

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x