add 4x to both sides
0=-24x³+10x²+4x
factor out the -2x from everybody
0=-2x(12x²-5x-2)
factor
use ac method
12 times -2=-24
what 2 numbers multiply to get -24 and add to get -5?
-8 and 3
0=-2x(12x²+3x-8x-2)
0=-2x((12x²+3x)+(-8x-2))
0=-2x(3x(4x+1)-2(4x+1))
0=-2x(3x-2)(4x+1)
set each to zero
0=-2x
0=x
0=3x-2
2=3x
2/3=x
0=4x+1
-1=4x
-1/4=x
x=-1/4 or x=0 or x=2/3
