(2y+1)(y+3)(5y-2)=0

If A x B x C=0, then A, B, or C are equal to zero. Therefore, for the problem, 2y+1=0
y+3=0
5y-2=0
Solving the equations for y will give the correct answers (three of them) for y.

To solve the given equation (2y+1)(y+3)(5y-2)=0, we can apply the zero product property, which states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero.

So, in this case, we can set each factor equal to zero and solve for y:

1. Set 2y+1=0:
Subtract 1 from both sides: 2y = -1
Divide both sides by 2: y = -1/2

2. Set y+3=0:
Subtract 3 from both sides: y = -3

3. Set 5y-2=0:
Add 2 to both sides: 5y = 2
Divide both sides by 5: y = 2/5

Therefore, the equation (2y+1)(y+3)(5y-2)=0 has three solutions for y: y = -1/2, -3, and 2/5.