factor 25x*2+30x+5 explain how to do this please?

5(5x^2 + 6x + 1)
5(x+1)(5x+1)

25x^2 + 30x + 5
= 5(5x^2 + 6x + 1)
= 5(5x^2 + 5x + x + 1)
= 5[(5x^2 + 5x) + (x + 1)]
= 5[5x(x + 1) + 1(x + 1)]
= 5(x + 1)(5x + 1)

Solution: 25x² + 30x + 5 = 5*(5x² + 6x + 1) = 5*(5x² + 5x + x + 1) = 5*[5x*(x + 1) + 1*(x + 1)] = 5*(5x + 1)*(x + 1)

Explanation: After factoring, you can see that if:
5(5x + 1)(x + 1) = 0
then, x = -1/5 or x = -1

We can propose that if we know this result, we'll be able to factor this thing easily. What result, you ask? The result that "when x = -1/5 or x = -1, the whole thing (25x² + 30x + 5) will receive the value of zero".

How do we know this? Grab an fx-500 MS calculator or better (I know you can afford one) and find your answer.
Plug in (25x² + 30x + 5) and you'll get that x = -1/5 or x = -1, that's what you need.

Now that you've got the results, time to factor:
- First, get the factor 5 out of the way:
25x² + 30x + 5 = 5*(5x² + 6x + 1)
- Next, create the "x + 1" factor (because x = -1 means x + 1 = 0)
5*(5x² + 5x + x + 1) <~~~ Why 6x = 5x + x? because 5x² + 5x = 5x*(x + 1), we need the x + 1.
- Next, factor (x + 1) out
5*[5x(x + 1) + 1*(x + 1)] <~~~ Why 1*(x + 1)? because when we factor (x + 1) out, we'll need the number 1 to add with 5x
- continue factoring:
5*(x + 1)(5x + 1).

Tada~