Question

Solve the following quadratic equations by factorization:

$16x-\frac{10}{x}=27$

Answer 1

$$\begin{gathered} 16x-\frac{10}{x}=27 \\ \Rightarrow 16x^2-10=27x \\ \Rightarrow 16x^2-27x-10=0 \\ \Rightarrow 16x^2-32x+5x-10=0 \\ \Rightarrow 16x\left(x-2\right)+5\left(x-2\right)=0 \\ \Rightarrow \left(16x+5\right)\left(x-2\right)=0 \\ \Rightarrow 16x+5=0\mathrm{or}x-2=0 \\ \Rightarrow x=-\frac{5}{16}\mathrm{or}x=2 \end{gathered}$$

Hence, the factors are $2$ and $-\frac{5}{16}$.