Question

$$f(x)=(3x-2),P(x)=3 { x }^{ 3 } + { x }^{ 2 } -20x+12$$

Answer

x=-2/(f-3),0

Solution


Remove parentheses.
\[\begin{aligned}&fx=3x-2\\&Px=3{x}^{3}+{x}^{2}-20x+12\end{aligned}\]
Break down the problem into these 2 equations.
\[fx=3x-2\]
\[fx=Px\]
Solve the 1st equation: \(fx=3x-2\).
\[x=-\frac{2}{f-3}\]
Solve the 2nd equation: \(fx=Px\).
\[x=0\]
Collect all solutions.
\[x=-\frac{2}{f-3},0\]