So somehow I tested into intermediate algebra and I’m doing pretty well except for this factoring quadratic equations by grouping thing. Could someone either explain it to me like I’m an idiot or point to an idiot level explanation?

Here’s were I’m at. Here’s a couple of examples. One I managed to solve, just not the right way, and one that left me pretty freaken confused.

The one I managed to solve on my own:

1/10R² - 5/2= 0

x10 to make everything whole. This left me with:

R² - 25 = 0

Looking at it now it was pretty obvious R = |5|, but algebra doesn’t have an intuition operator so I worked out this set of steps to show R = |5|:

+25 on both sides

R² = 25

Now I just have to squareroot it:

sqrt(R²) = sqrt(25)

The squareroote of R² is R, and 25 is 5 and -5.

Therefor R= -5, or 5

However the factoring by grouping way I scribbled down when someone asked in class:

1/10R² - 5/2= 0

x10 again, makes sense

R² - 25 = 0

Now here is where it gets crazy somehow we end up with:

(R+5)(R-5) = 0

Well obviously one of those is 0 since you can only get 0 from multiplication if 0 is one of the items being multiplied. Therfore R = -5, or +5, but where in the fire caves did (R+5)(R-5) = 0 come from?

I asked about this one:

3y² + 11y = 0

The steps were:

3y² + 11y = 0

(y+4)(3y-1) = 0

Y = -4, 3y-1= 0

Add one:

3y = 1

Divide by 3

Leaving us with:

Y= 1/3, and y = -4

I understand everything but the parentheses sets. Where do they come from? My attempts to figure this out say I need to find the greatest common factor, but what do I do with greatest common factor when I find it and where did the – 4 come from? It doesn’t seem to be a factor of anything. I’ve tried googling, reading, no go. Help?