The problem asks to factor the quadratic expression $6y^2 + 7y - 3$.

1. Problem Description

The problem asks to factor the quadratic expression $6y^2 + 7y - 3$.

2. Solution Steps

To factor the quadratic expression $6y^2 + 7y - 3$, we need to find two numbers that multiply to $6 \times -3 = -18$ and add up to $7$. These two numbers are $9$ and $-2$.

Now we rewrite the middle term using these two numbers:

$6y^2 + 7y - 3 = 6y^2 + 9y - 2y - 3$

Next, we factor by grouping:

$6y^2 + 9y - 2y - 3 = 3y(2y + 3) - 1(2y + 3)$

Finally, we factor out the common factor $(2y + 3)$:

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

3. Final Answer

The factored form of the quadratic expression $6y^2 + 7y - 3$ is $(3y - 1)(2y + 3)$.