#### Answer

$4a^{2}+10a+6=2(2a+3)(a+1)$

#### Work Step by Step

$4a^{2}+10a+6$
Express $10a$ as $2(5a)$:
$4a^{2}+10a+6=...$
$...=4a^{2}+2(5a)+6=...$
Open two parentheses including initially the square root of the first term, which is $2a$, followed by the sign of the second term, in the first parentheses and the product of the signs of the second and third term, in the second parentheses:
$(2a+)(2a+)$
Find two numbers whose product is equal to the third term, $6$ and whose sum is equal to the coefficient of the expression inside parentheses in the second term, $5$.
These two numbers are $3$ and $2$, because $(3)(2)=6$ and $3+2=5$
$...=(2a+3)(2a+2)=...$
Take out common factor $2$ from the second parentheses to finish the factoring process:
$...=2(2a+3)(a+1)$