\(pt\Leftrightarrow2x^3+5x^2-7x=0\)
\(\Leftrightarrow x\left(2x^2+5x-7\right)=0\)
\(\Leftrightarrow x\left(2x^2+7x-2x-7\right)=0\)
\(\Leftrightarrow x\left[x\left(2x+7\right)-\left(2x+7\right)\right]=0\)
\(\Leftrightarrow x\left(x-1\right)\left(2x+7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\\2x+7=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-\dfrac{7}{2}\end{matrix}\right.\)
\(2x^3+5x^2=7x\)
\(\Leftrightarrow2x^3-2x^2+7x^2-7x=0\)
\(\Leftrightarrow2x^2\left(x-1\right)+7x\left(x-1\right)=0\)
\(\Leftrightarrow\left(2x^2+7x\right)\left(x-1\right)=0\)
\(\Leftrightarrow x\left(2x+7\right)\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+7=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\2x=-7\\x=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{-2}{7}\\x=1\end{matrix}\right.\)
2x3+5x2=7x
=>2x3+5x2-7x=0
=>x(2x2+5x-7)=0
=>x(2x2+7x-2x-7)=0
=>x(2x2-2x)+(7x-7)=0
=>x(2x(x-1)+7(x-1))=0
=>x(x-1)(2x+7)=0
x=0 x=0
=> x-1=0 < => x=1
2x+7=0 x=-7/2
\(2x^3+5x^2=7x\)
\(\Rightarrow-7x+2x^3+5x^2=-7x+7x\)
\(\Rightarrow-7x+2x^3+5x^2=0\)
\(\Rightarrow x\left(-7+5x+2x^2\right)=0\)
\(\Rightarrow x\left(-7-2x\right)\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\-7-2x=0\\1-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{-7}{2}\\x=1\end{matrix}\right.\)
