factorise this equation x squared + 8x+15=0?

x^2 + 8x + 15 = 0
x^2 + 5x + 3x + 15 = 0
(x^2 + 5x) + (3x + 15) = 0
x(x + 5) + 3(x + 5) = 0
(x + 5)(x + 3) = 0

x + 5 = 0
x = -5

x + 3 = 0
x = -3

∴ x = -5, -3

With factorizing we need to turn it into something like (x+something)(x+something else) which equals x^2+8x+15. There are many ways to do this.

When we factorize these terms (assuming that the number in front of the x^2 is 1 or nothing in front at all) there's two numbers that add up to what's in front of the x that multiplies to be the end number. Let's call them a and b because using something and something else is tedious.
So these numbers have the properties that a+b=8 and a*b=15. The quickest way to find them is by looking at the second equation and looking for factors that might fit the bill. We'll need to consider negatives, just in case.
(a,b)=(1,15) or (-1,-15) or (3,5) or (-3,-5)
Lets add each pair up and see:
a+b=16 or -16 or 8 or -8
The third pair results in 8 so the two numbers we need are 3 and 5. Remember the a and b are replacing the something and something else in the brackets on the first line so the factorization becomes:
(x+3)(x+5)

Until you get the hang of this, it may be good to expand this out to check (if you don't know how to expand this check that the two numbers when added are the number in front of the x and multiplied together become the last number).

(x+5)(x+3)
x=(-3,-5)

( x + 5 ) ( x + 3 ) = 0

x = - 5 , x = - 3

x^2+8x+15=0
(x+5)(x+3)=0

Hope this helps!

we write x squared as x^2

so, the method is easy when there is no coefficient on the squared term. Look at the last term and think of the factors of 15 that add to 8. With a little thought, you realize it is 5 and 3.

So we write it like this,
(x + 5) (x + 3)

Expand this to verify.

x^2+8x+15=0
write 8x=3x+5x
thus we have
x^2+3x+5x+15=0
x(x+3)+5(x+3)=0
thus(x+3)(x+5)=0

i hope this helps thanx and may god bless u