Hiw do i completely factor 5x^2+36x+7=0

There is a method I use called the x method, I can’t show it to you but I will do my best to explain it

Basically, the factors of 5 and 7 must equal 36, so it’s kind of like cross multiplying

5 X 1

1 7

Five times seven equals 35

1 Times 1 equals 1

35 + 1 = 36

This is the answer:

(5x+1) (x+7)

You do 5 times 7 which equals 35. then you find factors of 35 that equal 36. 35x1=35 and 35 + 1 = 36. 5x^2 + 35x + 1x + 7 = 0 then you (5x^2 + 35x) (x + 7) and you can factor out a 5x out of the first one to get (x + 7) and the other stays (x + 7) and then you have (5x + 1) (x + 7) = 0 so you set each of them to zero and you get 5x + 1 = 0 which is x = - 1/5 and x + 7 = 0 which is x = - 7.