2021/065) Solve the biquadratic equation $(x-9)(x-7)(x+3)(x+5)= 1792$

Because (-7) -(-9) = 2 and and 5-3 = 3 let us take y to be mean of x- 7 and x + 3 that is x - 2

So get get

$(y-7)(y-5)(y+5)(y+7) = 1792$

or $(y-7)(y+7)(y-5)(y+5) = 1792$

or $(y^2-49)(y^2-25) = 1792$

or $y^4 - 74 y^2 + 1225 = 1792$

or $y^4-74 y^2 - 567=0$

or $(y^2-81)(y^2 + 7) = 0$ so $y^2=81$ as $y^2 \ge 0$

giving $y = \pm 9$ or $x \in \{ 11,7\}$ the solution set