Chapter 5 Polynomials and Polynomial Functions - 5.5 Apply the Remainder and Factor Theorems - 5.5 Exercises - Problem Solving - Page 368: 46

See below.

$x=2$ is a solution thus by the factor theorem $x-2$ is a factor of the equation, hence: $-6x^3+72x=96\\-x^3+12x=16\\-x^3+12x-16=0\\x^3-12x+16=0\\(x-2)(x^2+2x-8)=0\\(x-2)(x-2)(x+4)=0$ Thus the solutions are $x=2$ and $x=-4$ but $x\ne2$ and $x\gt0$, thus we have shown that there is no other option.