factor: $21y^2 - 2y - 3$

factor:
$21y^2 - 2y - 3$

We need two numbers that multiply to $21\times(-3)= -63$ and add up to $-2$. The numbers are $-9$ and $7$ since $-9\times7 = -63$ and $-9 + 7=-2$.

Rewrite $-2y$ as $-9y + 7y$ in the expression $21y^{2}-2y - 3$:
$21y^{2}-9y + 7y-3$

Group the first two terms and the last two terms:
$(21y^{2}-9y)+(7y - 3)$

Factor out $3y$ from the first group and $1$ from the second group:
$3y(7y - 3)+1(7y - 3)$

Factor out $(7y - 3)$ from both terms:
$(3y + 1)(7y - 3)$

$(3y + 1)(7y - 3)$