a) \(2x+5=0\)
\(\Rightarrow2x=-5\)
\(\Rightarrow x=-\dfrac{5}{2}\)
b) \(5x+\dfrac{3}{2}=0\)
\(\Rightarrow5x=-\dfrac{3}{2}\)
\(\Rightarrow x=-\dfrac{3}{2}:5=-\dfrac{3}{10}\)
c) \(2x^2-4x=0\)
\(\Rightarrow2x\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
d) \(\left(x-2\right)\left(x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
e) \(\left(2x-1\right)\left(x+\dfrac{3}{2}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=0\\x+\dfrac{3}{2}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=1\\x=-\dfrac{3}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
f) \(\left(x+5\right)\left(x^2+8\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+5=0\\x^2+8=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-5\\x^2=-8\left(\text{vô lí}\right)\end{matrix}\right.\)
g) \(x^2-5x+4=0\)
\(\Rightarrow x^2-x-4x+4=0\)
\(\Rightarrow x\left(x-1\right)-4\left(x-1\right)=0\)
\(\Rightarrow\left(x-4\right)\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=1\end{matrix}\right.\)
f) \(x^2-8x+15=0\)
\(\Rightarrow x^2-3x-5x+15=0\)
\(\Rightarrow x\left(x-3\right)-5\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(x-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-5=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=5\end{matrix}\right.\)
