Factorise and solve x^2 – 8x + 15 = 0

This equation is of the form ax² + bx + c = 0 (where a = 1, b = -8 and c = 15). To help solve it, find two numbers that add to give the value of b (the 'sum') and also when multiplied together give the same answer as a*c (the 'product'). 

For this equation, the sum = -8 and the product = 15.

Because the sum is negative and the product is positive we're looking for two negative numbers.

In this case they are -3 and -5, so the factorised equation would be: (x - 3)(x - 5) = 0.

In the factorised equation, the two bracket terms are multiplied together, so to solve the equation, make one of the brackets equal zero. 

The two 'roots' of the equation, i.e. the values of x that make the equation true, are x = 3 and x = 5.