Solve the equation by factoring $$ x^{2}=3 x+28 $$ The solution set is $$ \{\square\} $$ (Use a comma to separate answers as needed. Type each solution only once )

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To solve the equation $$ x^{2} = 3x + 28 $$ by factoring, follow these steps:

1. **Move all terms to one side of the equation:**
   $$
   x^{2} - 3x - 28 = 0
   $$

2. **Factor the quadratic equation:**
   We need to find two numbers that multiply to $$-28$$ and add up to $$-3$$. These numbers are $$-7$$ and $$4$$.

$$
   (x - 7)(x + 4) = 0
   $$

3. **Find the solutions:**
   Set each factor equal to zero and solve for $$x$$:
   $$
   x - 7 = 0 \quad \Rightarrow \quad x = 7
   $$
   $$
   x + 4 = 0 \quad \Rightarrow \quad x = -4
   $$

4. **Write the solution set:**
   $$
   \{ -4, 7 \}
   $$

**Final Answer:**
$$\{ -4, 7 \}$$
The solutions are $$ x = -4 $$ and $$ x = 7 $$.

Solve the equation by factoring \( x^{2}=3 x+28 \) The solution set is \( \{\square\} \) (Use a comma to separate answers as needed. Type each solution only once )

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