Answer
$15y^{2}+y-2=(5y+2)(3y-1)$
Work Step by Step
$15y^{2}+y-2$
Since the coefficient of $y^{2}$ is not equal to $1$, begin by multiplying the whole expression by $15$, which is the actual coefficient of $y^{2}$. Leave the product between $15$ and the second term expressed:
$15(15y^{2}+y-2)=...$
$...=225y^{2}+15(y)-30$
Open two parentheses containing initially the square root of the second term, which is $15y$, followed by the sign of the second term, in the first parentheses, and the product of the signs of the second and third terms, on the second parentheses:
$...=(15y+)(15y-)$
Find two numbers whose product is equal to the third term, $-30$ and whose sum is equal to the coefficient of the expression inside parentheses in the second term, $1$.
These two numbers are $6$ and $-5$, because $(6)(-5)=-30$ and $6-5=1$.
$...=(15y+6)(15y-5)$
The expression was affected initially by multiplying it by $15$. Divide it by $15$ to obtain the answer:
$...=\dfrac{(15y+6)(15y-5)}{15}=...$
Substitute $15$ by $3\cdot5$ and divide the first parentheses by $3$ and the second parentheses by $5$:
$...=\dfrac{(15y+6)(15y-5)}{3\cdot5}=...$
$...=\dfrac{(15y+6)}{3}\dfrac{(15y-5)}{5}=...$
$...=(5y+2)(3y-1)$
