How do you factorize a quadratic when a ≠ 1 when ax²+bx+c=0

First check if a, b and c all have a common factor.For example, if we have 3x²+6x+3=0, we can divide both sides by 3 and get x²+2x+1=0, which is easier to solve.If a,b and c do not all have a common factor we can solve it by working backwards.For example, if we have 2x²+3x-9=0 we already know the factorization has to be in the form (2x+i)(x+j)=0in this case we look at all the factors of -9 and we see which pairs of factors i and j satisfy the equation i+2j=3After doing this we find that 2x²+3x-9 = (2x-3)(x+3)