There are a few ways to evaluate a quadratic equation when the lead term's coefficient is a number besides a 1. In this case it's a 6. I think this is by far, the easiest approach:
[Step 1: multiply the lead term to the last term] *don't forget we did this, as we'll have to reverse it at the end:
6x²+11x+4:
x²+11x+24 [Step 2: factor normally]
Factors of 24 which add to 11 are 8 and 3
(x+8) (x+3)
However, we have to address the 6 that we multiplied at the beginning...[step 3]: divide the 6 from the numbers in each of the binomials:
(x+8/6) (x+3/6)
[Step 4]: Reduce each fraction. We can divide out a 2 from the first fraction, and a 3 from the second fraction:
(x+4/3)(x+1/2).
[Step 5]: Move any remaining denominator value in front of the x-terms:
(3x+4)(2x+1)
And, we're done!
