x^2 + 2x - 15 = 0
To solve this equation (i.e. to find the value of x), you need to factorise it:
To factorise an equation you need to look at the multiples of the number without any 'x'.
In your equation this is -15.
So multiples of 15 are: 1x15, 3x5.
You then choose the multiples that will equal the term with the 'x' , when added. To do this you need to take into account the fact that for your equation the last term is negative.
So the only possible choice for this equation is 3 and 5 (as the term '2x' can never be gained by adding or subtracting 1 and 15).
And so now (because we need -15) the only possible choices are:
(x - 3)(x + 5) or (x + 3)(x - 5)
Now if you imagine multiplying out the brackets you can see that the only choice that is going to give the right answer is: (x - 3)(x + 5)
x^2 + 2x - 15 = (x - 3)(x + 5) = 0
And so now you can see that the only times when this equation is going to equal zero is when: x = 3 or x = -5 , and this is the final solution to the equation.