**find all values of x satisfying the given conditions: y=2x^3+x^2-8x+2 and y = 6.**

**Answer:**

putting the value of y in the 1st equation, we get

2x^3+x^2-8x-4=0

try putting x=-1, 1 to see if they satisfy the equation. They dont.

For solving cubic equations, first one needs to check if -2, -1, 1, 2 satisfy the equation.

In this case, -2 and 2 satisfy the equation. So, the answers are 2 and -2.

y=2x^3+x^2-8x+2 and y = 6

6=2x^3+x^2-8x+2

0=2x^3+x^2-8x-4

0=(2x^3+x^2)+(-8x-4)

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

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

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

x=2,-2,-0.5

-0.5 however doesnâ€™t fit into the equation properly, so, therefore, the final answers are -2 and 2.