List all possible solutions to the following equations.
`(y-3)(y+6)=0`

Answer

To solve the equation \((y-3)(y+6)=0\), we will follow these steps:

### Step 1: Set each factor equal to zero
Since the product of two factors is zero, we can set each factor equal to zero:
1. \(y - 3 = 0\)
2. \(y + 6 = 0\)

### Step 2: Solve the first equation
Now, let's solve the first equation:
\[ y - 3 = 0 \]
Adding 3 to both sides gives:
\[ y = 3 \]

### Step 3: Solve the second equation
Next, we solve the second equation:
\[ y + 6 = 0 \]
Subtracting 6 from both sides gives:
\[ y = -6 \]

### Step 4: List all possible solutions
The solutions to the equation \((y-3)(y+6)=0\) are:
\[ y = 3 \quad \text{and} \quad y = -6 \]

### Final Answer
Thus, the possible solutions to the equation are:
\[ \boxed{3 \text{ and } -6} \]

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