Find the $$ x $$ and $$ y $$ intercept of following: $$ y=(x-3)(x+4 $$

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To find the $$ x $$ and $$ y $$ intercepts of the given equation $$ y = (x-3)(x+4) $$, we need to set $$ y = 0 $$ to find the $$ x $$ intercepts and set $$ x = 0 $$ to find the $$ y $$ intercept.

1. To find the $$ x $$ intercepts, set $$ y = 0 $$:
$$ 0 = (x-3)(x+4) $$

2. To find the $$ y $$ intercept, set $$ x = 0 $$:
$$ y = (0-3)(0+4) $$

Let's solve these equations to find the intercepts.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$0=\left(x-3\right)\left(x+4\right)$$
- step1: Swap the sides:
  $$\left(x-3\right)\left(x+4\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-3=0\&x+4=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=3\&x=-4\end{align}$$
- step4: Rewrite:
  $$x_{1}=-4,x_{2}=3$$
The $$ x $$ intercepts of the given equation $$ y = (x-3)(x+4) $$ are $$ x = -4 $$ and $$ x = 3 $$.

Now, let's find the $$ y $$ intercept by setting $$ x = 0 $$ in the equation.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$y=-12$$
The $$ y $$ intercept of the given equation $$ y = (x-3)(x+4) $$ is $$ y = -12 $$.

Therefore, the $$ x $$ intercepts are $$ x = -4 $$ and $$ x = 3 $$, and the $$ y $$ intercept is $$ y = -12 $$.
The $$ x $$-intercepts are $$ x = -4 $$ and $$ x = 3 $$, and the $$ y $$-intercept is $$ y = -12 $$.

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