Question

Solve the equation :$x^3-6x^2+8x=0$

Short answer

The solution of the equation is$x=0,2,4$

Step-by-step solution

Given information

We are given an equation$x^3-4x^2+8x=0$

We separate the terms

We have,

$$\begin{gathered} x^3-6x^2+8x=0 \\ x(x^2-6x+8)=0 \\ x=0or{x}^2-6x+8=0 \end{gathered}$$

Now solve the quadratic equation

We get,

$$\begin{gathered} x^2-6x+8=0 \\ {x}^2-4x-2x+8=0 \\ x(x-4)-2(x-4)=0 \\ (x-4)(x-2)=0 \\ x=4orx=2 \end{gathered}$$

Conclusion

The roots of the given equation are$x=0,2,4$