Y^2+8y+15=0 use factorization to solve for the unknown

To factorize Y^2+8y+15=0, we need to find two numbers that add up to 8 and multiply to 15. These numbers are 3 and 5. Therefore, we can write:

Y^2+8y+15 = (Y+3)(Y+5) = 0

Now we can use the zero product property, which states that if a product of two factors is equal to zero, then at least one of the factors must be zero. Therefore, we have:

Y+3 = 0 or Y+5 = 0

Solving for Y, we get:

Y = -3 or Y = -5

Therefore, the solutions of Y^2+8y+15=0 are Y=-3 and Y=-5.