Solve by applying the zero product property. $$ m^{2}+4 m=21 $$ If there is more than one solution, separate the answers with commas.

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation $$ m^{2} + 4m = 21 $$ using the **zero product property**, follow these steps:

1. **Move all terms to one side of the equation:**

$$
   m^{2} + 4m - 21 = 0
   $$

2. **Factor the quadratic expression:**

We need two numbers that multiply to $$-21$$ and add up to $$4$$. Those numbers are $$7$$ and $$-3$$.

$$
   (m + 7)(m - 3) = 0
   $$

3. **Apply the zero product property:**

If the product of two factors is zero, then at least one of the factors must be zero.

$$
   m + 7 = 0 \quad \text{or} \quad m - 3 = 0
   $$

4. **Solve for $$ m $$:**

- For $$ m + 7 = 0 $$:
     $$
     m = -7
     $$
   
   - For $$ m - 3 = 0 $$:
     $$
     m = 3
     $$

**Solutions:** $$-7, 3$$
The solutions are $$ m = -7 $$ and $$ m = 3 $$.

Solve by applying the zero product property.

If there is more than one solution, separate the answers with commas.