2x²+22x+60 how would you factor it completely

All these numbers are even numbers, so we know immediately we can cut them down in side. 2 is the smallest they can be cut down, so let's divide all the numbers by 2. In general smaller numbers are easier to work with.

2 (x^2 + 11x + 30)

Now, we need to find a product of 30 that adds up to 11. (ie x * y = 30 where x+y = 11).

This idea is just a part of the 'formula' for figuring out factors. The middle number is the sum of the factors of the last number.

This is a trial and error thing. I generally start with the easiest, which might be 2 in this case. That breaks down to 15 * 2, but adding those together gets us 17, so that's wrong.

The next easiest number is 5. 30/5 = 6, so does 6 + 5 = 11? Yep! That's our factor.

Now, we rewrite the equation with our factored amounts. We have to start with 2, because we cut that out in the beginning.

2 (? + ?) (? + ?)

Our first part is x^2. We know the only way to get that is x * x, so we fill those in the start.

2 (x + ?) (x + ?)

We add in our factors into the missing parts. The order does not matter.

2 (x + 6) (x + 5)

Factor out the common factors

(2) (x^2+11x+30)

find what 2 numbers multiply to get 30 and add to get 11

factor 30

factors of 30 are

1,30

2,15

3,10

5,6

add them togethers

1+30=31

2+15=17

3+10=13

5+6=11 match

the numbers are 5 and 6

(x+6) (x+5)

the factored out form is (2) (x+6) (x+5)

if it was equal to zero then the solution would be - 6 and - - 5