Question

HOW TO FACTOR 20X^2+23X-21 STEP BY STEP

Answer 1

you have

20x^2 + 23x - 21
if p/q is a root, then p divides 21 and q divides 24. So, there will be lots of things to try.

since the 20 and 23 are sort of close to each other, try factors of 20 that are sort of close: 4 and 5

(4x+?)(5x-?) or (4x-?)(5x+?)
the ?'s will divide 21, but it's basically trial and error. A bit of effort will show that (4x+7)(5x-3) works

Usually with messy one like this, the good old quadratic formula is easiest

x = (-23 ± √(23^2 + 4*20*21))/40
x = (-23 ± √(2209))/40
x = (-23 ± 47)/40
x = 24/40 or -70/40

so,
(40x-24) = 0
(40x+70) = 0
pull out factors to get
(5x-3) = 0
(4x+7) = 0
Those are the factor