Solve the quadratic 3x^2+11x+6=0

In order to solve the quadratic, we need to factorise it. Consider the coefficient on the x^2, its only factors are 1 and 3 so this tells us that in our factorising we will have something that looks like (x...)(3x...). All the signs are positive so we know that it will also be a case of positive numbers (x+...)(3x+...).

Consider the factors of 6, by looking i can see that a combination on 3 and 2 is going to add up to get to 11 as 3x3=9 and x2=2x which totals 11x. Hence we have (x+3)(3x+2)=0. From that, I can show that my solutions will be x=-3, -2/3 after equating each bracket to 0.