solve X^2-x-12=0

To solve this equation we will want to first factorise the expression into two brackets, and then see what value makes each bracket 0. transform X^2-X-12=0 into (X+c)(X+d)=0We do this by finding factor pairs of -12 and testing whether they summate to -1 (the value of the middle x part of the equation)these Pairs are:3 and -4, 4 and -3, 12 and -1, 1 and -12, 6 and -2, 2 and -6.the first pair we test produces the result -1 which is what we want. so (X+c)(x+d)=0 becomes (X+3)(x-4)=0.Finally, we need the values of x which makes each bracket 0. in the first bracket, -3 is required. in the second, 4 is required.so X=-3, 4