The solutions of the given cubic equation are (x = -8), (x = -4), and (x = 6) and this can be determined by using the factorization method.
Given :
Equation is [tex]x^3+6x^2-40x=192[/tex].
The following steps can be used in order to determine the solution(s) to the given equation:
Step 1 - Write the given equation.
[tex]x^3+6x^2-40x=192[/tex]
Step 2 - Rewrite the above equation.
[tex]x^3+6x^2-40x-192=0[/tex]
Step 3 - Now, factorize the above equation.
[tex]\begin{aligned}\\x^3-6x^2+12x^2-72x+32x-192&=0\\(x^2+12x+32)(x-6)&=0\\\end{aligned}[/tex]
Step 4 -Again factorize the above equation.
[tex]\begin{aligned}\\(x-6)(x^2+8x+4x+32)&=0\\(x-6)(x+8)(x+4)&=0\\\end{aligned}[/tex]
Therefore, the correct options are A), B), and C).
For more information, refer to the link given below:
https://brainly.com/question/6810544
