Factorise:
`7y^(2) - 19y -6`

Answer

To factorise the expression \( 7y^2 - 19y - 6 \), we can follow these steps:

### Step 1: Identify the coefficients
The expression is in the form \( ay^2 + by + c \), where:
- \( a = 7 \) (coefficient of \( y^2 \))
- \( b = -19 \) (coefficient of \( y \))
- \( c = -6 \) (constant term)

### Step 2: Multiply \( a \) and \( c \)
We need to multiply \( a \) and \( c \):
\[ 7 \times (-6) = -42 \]
Now we need to find two numbers that multiply to \(-42\) and add up to \(-19\).

### Step 3: Find the two numbers
The two numbers that satisfy these conditions are \(-21\) and \(2\) because:
\[ -21 \times 2 = -42 \quad \text{and} \quad -21 + 2 = -19 \]

### Step 4: Rewrite the middle term
Now we can rewrite the expression \( 7y^2 - 19y - 6 \) by splitting the middle term using the two numbers we found:
\[ 7y^2 - 21y + 2y - 6 \]

### Step 5: Group the terms
Next, we group the terms:
\[ (7y^2 - 21y) + (2y - 6) \]

### Step 6: Factor out the common factors
Now we factor out the common factors from each group:
\[ 7y(y - 3) + 2(y - 3) \]

### Step 7: Factor by grouping
Now we can factor out the common binomial factor \((y - 3)\):
\[ (7y + 2)(y - 3) \]

### Final Answer
Thus, the factorised form of \( 7y^2 - 19y - 6 \) is:
\[ (7y + 2)(y - 3) \]