Question
Solve equation by factorization $:\frac{x^2}{15}-\frac{x}{3}-10=0$
✓
Answer
$\frac{x^2}{15}-\frac{x}{3}-10=0$
$\Rightarrow x^2-5 x-150=0 \ldots\left\{\begin{array}{l}\because-150=-15 \times 10 \\ -5=-15+10\end{array}\right\}$
$\Rightarrow x^2-15 x+10 x-150=0$
$ \Rightarrow x(x-15)+10(x-15)=0$
$ \Rightarrow(x-15)(x+10)=0$
Elther $x-15,$
then $x=15$
or
$x+10=0$
then $x=-10$
$\therefore x=15,-10 \text {. }$
$\Rightarrow x^2-5 x-150=0 \ldots\left\{\begin{array}{l}\because-150=-15 \times 10 \\ -5=-15+10\end{array}\right\}$
$\Rightarrow x^2-15 x+10 x-150=0$
$ \Rightarrow x(x-15)+10(x-15)=0$
$ \Rightarrow(x-15)(x+10)=0$
Elther $x-15,$
then $x=15$
or
$x+10=0$
then $x=-10$
$\therefore x=15,-10 \text {. }$
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