Solve the equation. Express numbers in exact simplest form. $$ 3 y(y+3)=12 $$ The solution set is $$ \{\square\} $$.

Question

UpStudy AI · Accepted Answer

We start with the equation:

$$
3y(y+3) = 12
$$

**Step 1. Expand the left-hand side**

$$
3y^2 + 9y = 12
$$

**Step 2. Bring all terms to one side**

$$
3y^2 + 9y - 12 = 0
$$

**Step 3. Divide the entire equation by 3 to simplify**

$$
y^2 + 3y - 4 = 0
$$

**Step 4. Factor the quadratic equation**

We look for two numbers that multiply to $$-4$$ and add to $$3$$. These numbers are $$4$$ and $$-1$$.

$$
y^2 + 3y - 4 = (y + 4)(y - 1)
$$

**Step 5. Use the Zero-Product Property**

Set each factor equal to zero:

$$
y + 4 = 0 \quad \text{or} \quad y - 1 = 0
$$

Thus, the solutions are:

$$
y = -4 \quad \text{or} \quad y = 1
$$

**Answer:**

The solution set is $$ \{-4, 1\} $$.
The solutions are $$ y = -4 $$ and $$ y = 1 $$.

Solve the equation. Express numbers in exact simplest form. \[ 3 y(y+3)=12 \] The solution set is \( \{\square\} \).