Solve - 4x=10x^2-24x^3

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