When factorizing a quadratic function look for factors of the square coefficient (in this case 6) and factors of the constant term (in this case 1).
In this case the coefficient of the y term is negative and the constant term is positive, so the constants in each of the factors must both be negative. Since the constant is +1, its factors must be -1 and -1.
Integer factors of 6, independent of order, are
(1,6); (2,3); ("-"1,"-"6); ("-"2,"-"3)
Now look for the factor pair that when multiplied by (-1, -1) sums to -5. Here this is (2,3). These are the coefficients of the y terms in each factor.
Hence, the factors are (2y-1) and (3y-1).
Note: Not all quadratic functions can be factorized.
