Solve the equation using the zero-product principle. $$ (x-9)(4 x+9)=0 $$ The solution set is $$ \left\{\begin{array}{l}\text {. }\end{array}\right. $$ (Use a comma to separate answers as needed.)

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Solve the equation $$ (x-9)(4x+9)=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$\left(x-9ight)\left(4x+9ight)=0$$
- step1: Separate into possible cases:
  $$\begin{align}&x-9=0\&4x+9=0\end{align}$$
- step2: Solve the equation:
  $$\begin{align}&x=9\&x=-\frac{9}{4}\end{align}$$
- step3: Rewrite:
  $$x_{1}=-\frac{9}{4},x_{2}=9$$
The solutions to the equation $$(x-9)(4x+9)=0$$ using the zero-product principle are $$x=-\frac{9}{4}$$ or $$x=9$$.

Therefore, the solution set is $$\{-\frac{9}{4}, 9\}$$.
The solution set is $$\{-\frac{9}{4}, 9\}$$.

Solve the equation using the zero-product principle. \[ (x-9)(4 x+9)=0 \] The solution set is \( \left\{\begin{array}{l}\text {. }\end{array}\right. \) (Use a comma to separate answers as needed.)

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