How do I solve a trinomial

Question

It tells me to solve -4x=10x^2-24x^3 and also says that there is 3 answers

Answer 1

y=-24x^3+10x^2+4x

let y=0

-24x^3+10x^2+4x=0

24x^3-10x^2-4x=0

divide all terms by 2

12x^3+5x^2+2x=0

factor out an "x"

x(12x^2-5x-2)=0

factor

12*2=2*2*3*2=(2*2*2)*3=8*3 and 8-3=5

x(4x+1)(3x-2)=0

x=0

4x+1=0

4x=-1

x=-1/4

3x-2=0

3x=2

x=2/3

solutions: x=0, -1/4, and 2/3

 

 

 

Answer 2

There are so many ways but the easiest way if you have a graphing calculator, graph y=10x^2-24x^3+4x and find the intersections where y=0. And yes there are 3 answers. Y=0 when x=-0.25, 0, and 0.667.