College Algebra (10th Edition)

$\color{blue}{\bf x=\left\{0, 2, 4\right\}}$
Factor the polynomial completely to obtain: $x(x^2-6x+8) = 0 \\x(x-4)(x-2)=0$ Equate each factor to zero, then solve each equation to obtain: \begin{array}{ccccc} &x=0 &\text{or} &x-4=0 &\text{or} &x-2=0 \\&x=0 &\text{or} &x=4 &\text{or} &x=2 \end{array} Thus, the solutions to the given equation are: $\color{blue}{\bf x=\left\{0, 2, 4\right\}}$