Simplify √-y to √yi
3+ 2y = √yi
Square bot sides
(3 + 2y)^2 = -y
Expand
9 + 12y + 4y^2 = -y
Move all terms to one side
9 + 12y + 4y^2 + y = 0
Simplify 9 + 12y + 4y^2 + y to 9 + 13y + 4y^2
9 + 13y + 4y^2 = 0
Split the second term in 9 + 13y + 4y^2 into two terms
4y^2 + 9y + 4y + 9 = 0
Factor out common terms in the first two terms, then in the last two terms
y(4y + 9) + (4y + 9) = 0
Factor out the common term 4y + 9
(4y + 9)(y + 1) = 0
Solve for y
y = -9/4, -1
Check solution
when y = -9/4, the original equation; 3 + 2y = √-y does not hold true. We will drop y = -9/4 from the solution set.
Therefore,
y = -1