When expanding brackets, we need to make sure each of the terms in the first bracket are multiplied by all the terms in the second bracket (and vice versa). To make sure nothing is missed, we can used the FOIL method (First Outer Inner Last). We start by multiplying the first two terms of each bracket together; 3X x X = 3X^{2} . We then multiply the outer terms together; 3X x -6 = -18X . Now multiply the innermost terms together; 9 x X = 9X . Finally, we multiply the last terms in each bracket together; 9 x -6 = -54 . Now the whole equation reads; 3X^{2 }- 18X + 9X - 54 = 0. Now collect like terms together; 3X^{2} - 9X - 54 =0

To simplify the equation, we must find a common multiple for each term. In this case we can divide each term by 3. This leaves the final and simplified answer as; X^{2} - 3X - 18 =0