Question

Solve:
$a(x^2+4)=x(a^2+4)$

Answer 1

$a(x^2+4)=x(a^2+4)$

$\Rightarrow a{x}^2+4a-x{a}^2-4x=0$

$\Rightarrow a{x}^2-a^{2}x-4x+4a=0$

$\Rightarrow ax(x-a)-4(x-a)=0$

$\Rightarrow (ax-4)(x-a)=0$

$\Rightarrow ax=4,x=a$

$\therefore x=\frac{4}{a},a$