I.` 5x^(2) + 28x + 15 = 0`
II.` 6y^(2) + 35y + 25 = 0`

Options

A. If`x gt y`
B. If`y gt x `
C. If`x ge y`
D. If x = y or a relationship between x and y cannot be established.

Explanation

To solve the equations \( 5x^2 + 28x + 15 = 0 \) and \( 6y^2 + 35y + 25 = 0 \), we will use the method of factorization.

### Step 1: Solve for \( x \) in the equation \( 5x^2 + 28x + 15 = 0 \)

1. **Identify the product of the coefficient of \( x^2 \) and the constant term**:
\[ 5 \times 15 = 75 \]

2. **Find two numbers that multiply to 75 and add up to 28**:
The numbers are 25 and 3 because:
\[ 25 + 3 = 28 \quad \text{and} \quad 25 \times 3 = 75 \]

3. **Rewrite the equation using these numbers**:
\[ 5x^2 + 25x + 3x + 15 = 0 \]

4. **Group the terms**:
\[ (5x^2 + 25x) + (3x + 15) = 0 \]

5. **Factor out the common terms**:
\[ 5x(x + 5) + 3(x + 5) = 0 \]

6. **Factor by grouping**:
\[ (5x + 3)(x + 5) = 0 \]

7. **Set each factor to zero**:
\[ 5x + 3 = 0 \quad \Rightarrow \quad x = -\frac{3}{5} \]
\[ x + 5 = 0 \quad \Rightarrow \quad x = -5 \]

### Step 2: Solve for \( y \) in the equation \( 6y^2 + 35y + 25 = 0 \)

1. **Identify the product of the coefficient of \( y^2 \) and the constant term**:
\[ 6 \times 25 = 150 \]

2. **Find two numbers that multiply to 150 and add up to 35**:
The numbers are 30 and 5 because:
\[ 30 + 5 = 35 \quad \text{and} \quad 30 \times 5 = 150 \]

3. **Rewrite the equation using these numbers**:
\[ 6y^2 + 30y + 5y + 25 = 0 \]

4. **Group the terms**:
\[ (6y^2 + 30y) + (5y + 25) = 0 \]

5. **Factor out the common terms**:
\[ 6y(y + 5) + 5(y + 5) = 0 \]

6. **Factor by grouping**:
\[ (6y + 5)(y + 5) = 0 \]

7. **Set each factor to zero**:
\[ 6y + 5 = 0 \quad \Rightarrow \quad y = -\frac{5}{6} \]
\[ y + 5 = 0 \quad \Rightarrow \quad y = -5 \]

### Summary of Solutions
- The values of \( x \) are \( -\frac{3}{5} \) and \( -5 \).
- The values of \( y \) are \( -\frac{5}{6} \) and \( -5 \).