Factorise x2+16x+15 completely.

Sure, here are the steps to factorise the given quadratic equation:

1. Identify the coefficients in the quadratic equation. In the equation x^2 + 16x + 15, the coefficient of x^2 is 1 (a), the coefficient of x is 16 (b), and the constant term is 15 (c).

2. Look for two numbers that multiply to give ac (in this case, 115 = 15) and add up to give b (in this case, 16). The numbers that satisfy these conditions are 15 and 1 because 151 = 15 and 15+1 = 16.

3. Rewrite the middle term of the quadratic equation (16x) as the sum of the terms 15x and x. This gives us the equation x^2 + 15x + x + 15.

4. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x^2 + 15x) + (x + 15).

5. Factor out the greatest common factor from each group. From the first group, we can factor out x, and from the second group, we can factor out 1. This gives us x(x + 15) + 1(x + 15).

6. Notice that the terms in parentheses are the same. We can factor out the common binomial term to give the final factorised form of the equation: (x + 15)(x + 1).

So, the factorised form of the equation x^2 + 16x + 15 is (x + 15)(x + 1).